Critical Fallibilism Terminology and Partial Truth
Many statements that contradict Critical Fallibilism are reasonable approximations.
Critical Fallibilism (CF) says to evaluate ideas as refuted or non-refuted using decisive, critical arguments. And CF says to evaluate ideas in the context of {idea, goal, context} (IGC) triples, so the same idea can have multiple evaluations. CF follows Critical Rationalism (CR) in denying the effectiveness of positive (justifying) arguments or induction. CF agrees with CR about accepting fallibilism and denying the possibility of absolute proof. CF adds that arguments don't have strengths: either they refute an IGC or they don't refute it. There's no partial refutation; indecisive arguments simply don't refute IGCs; arguments that can't decisively refute anything don't get partial credit.
However, many CF-incompatible things people say are reasonable statements which are in some sense approximately correct. Instead of rejecting them as false, we can translate or convert them to CF concepts. Often, some sort of translation will be easy and successful, so the original statement was actually basically fine even though it contradicted CF principles.
For example, people make positive arguments. They say "Going to a restaurant is a good idea because I'm hungry." This gives a positive reason (addressing hunger) in favor of a conclusion (going to a restaurant). CF says that's an error. But it can easily be translated to a negative argument to be compatible with CF. "Not going to a restaurant is a bad idea because I'm hungry." Now it's a criticism of many but not all alternatives to going to a restaurant.
In general, when a positive argument says "A is good because it has trait B", it can be reframed negatively as "Alternatives to A which lack trait B are bad". This is more precise for various reasons that CR discussed and because some alternatives also have trait B. This argument only helps A against some alternatives. Or in other words, it's a criticism of a category of alternatives but it doesn't criticize some other alternatives at all. Viewing it as a positive argument for A obscures that it's actually a criticism of B but not a criticism of C: it does nothing to make A better than C.
We can make this more precise again. The real issue is "A is good because it has trait B which addresses problem P". The negative version is "Alternatives to A which lack any solution to P are bad." An alternative with trait B is fine and an alternative with some other solution to P (to the same problem that B addresses) is also fine. You could also list multiple separate problems that B addresses instead of treating it as one problem, but the number of problems isn't important (it depends on how you conceptually organize and count the problems rather than having any fundamental importance).
If there is no way to translate a positive argument to a negative version, then the argument is wrong. If there's a straightforward translation (as there frequently is), then using positive arguments doesn't matter much when you're talking informally about any topic other than epistemology itself and things are going smoothly. When conversations are difficult or rigorous, then being more precise and using negative arguments directly with no translations needed can help. In difficult conversations, it's important to communicate clearly and reduce the guessing what you mean that other people have to do. And when you're talking about the logic of how arguments work and other epistemology topics, then understanding they're properly negative is important.
What about calling an idea "mostly true" or "mostly false"? This is frequently a reasonable approximation. "Mostly true" means "many but not all relevant IGCs containing this idea are non-refuted". "Mostly false" means "many but not all relevant IGCs containing this idea are refuted". Why is "relevant" specified? Because for any idea, as a matter of logic, looking at the set of all possible IGCs, it's in infinitely many true IGCs and infinitely many false IGCs. When we evaluate ideas, we might consciously consider a dozen IGCs that are relevant to us. We might subconsciously consider a few thousand IGCs (I don't know how to count that accurately). Whatever the numbers, we pick some IGCs that are intended to be relevant and don't consider infinitely many others. When we evaluate what percentage of IGCs are non-refuted, it's of the selection of IGCs we're looking at, which we've chosen for relevance, and which hopefully are a representative sample of all relevant IGCs.
What is a "good idea"? An idea that is in some relevant non-refuted IGCs. A "bad idea" is in some relevant refuted IGCs. These terms aren't very specific or precise, but sometimes that's OK; not all language needs to be precise. Sometimes we speak imprecisely about one thing when our focus is on something else. More precision isn't always better.
What is a "weak argument"? It sounds like an indecisive argument that doesn't refute anything. But we can translate it to mean an argument that refutes some of the relevant IGCs we're considering (maybe 20% of them). Similarly, a "strong argument" might refute 80% of relevant IGCs.
It's not a random accident, nor good luck, that this kind of conventional, mainstream terminology tends to easily translate to more precise statements. And it's not a design feature of CF to allow translations either. CF was designed to get at the truth in epistemology, not designed around enabling translations. No changes at all were made to CF's epistemology claims to help make translation easier. The reason translations are often easy is that mainstream statements about arguments aren't nonsense. They are meaningful, coherent, decent statements. Although the precise logic of them is wrong (because they use positive arguments, indecisive arguments and indecisive evaluations), most of the content is still fine (at least when people were making good points; when people are making bad points, translation won't yield a good point and may either fail or yield something that's more obviously a bad point which the speaker may be unhappy with). Because what people are saying is often reasonable, their statements can often be translated to a better epistemology and still say something useful.
We don't need to be very picky about terminology unless we're talking about epistemology, we're doing something really hard where we have to try our very best, or we're struggling or stuck in a conversation. And for most conversations that are going poorly, bringing up CF epistemology and trying to be more precise in this way won't help. It's only for certain types of intellectual conversations that you can reasonably expect introducing a bunch of advanced philosophy to help. Bringing up CF epistemology and using more precise phrasing regarding arguments can also more realistically help with far more conversations if all participants are already familiar with CF. Talking about IGCs and refutations works well for any topic if everyone already knows how to do it, but introducing it as a new thing to learn about can be a big distraction.
Note: While learning about CR or CF, it makes sense to look for contradictions even if they're just terminology issues not substantive problems. It's important to learn to identify when arguments are phrased positively or indecisively. It's important to get practice at translating statements into more precise, CF-compatible words. As you get good at that, you can develop some understanding of when the translation is useful and important, and when it's unnecessary to bring up. When you're new at it, you can try translating everything to get practice and learn when it's useful or not. But in some non-philosophical situations you can keep your practice to yourself (or go talk about it on the CF forum); it's generally not necessary to bug non-philosophers about it. If learning CF, you should learn to be aware of when you or others use approximate terminology that could be translated; ignoring it as unimportant, and never learning to notice half of it, wouldn't be good.
If non-CF statements can be translated to CF, does it matter which we use? Is CF any better? In casual, non-intellectual contexts, it usually doesn't matter that much. It's often easier to just speak in conventional terminology that everyone present is familiar with. That can be good enough for what you're doing.
In a context like scientific research, if everyone would learn about CF and start speaking in terms of IGCs and decisive refutations, it would help. It'd let people see the key issues more directly and precisely. Reasoning directly about IGCs can help people with decision making and evaluating ideas. Mainstream epistemology can be kind of fuzzy and leave people unsure what next steps to take while CF can make it easier to make progress. Mainstream epistemology struggles at getting decisive conclusions about disagreements between ideas.
CF can help with organizing debates and getting clearer outcomes, in science or in other matters. But don't use it to win debates with people who aren't familiar with it. It's fair to bring up CF in epistemology debates. But if you're debating biology, you shouldn't win just because you know about CF and therefore know more about the nature of arguments. Knowing more about arguments itself can give you an advantage in debate, but it's bad to win a debate when your ideas about the topic (e.g. biology) are actually worse than the other guy's. Don't use the power of CF to try to make up for the weakness of your topical knowledge. Don't use other people's ignorance of CF to try to make them seem wrong when their ideas can actually be easily translated to CF and the ideas are actually good. But also, if everyone in the debate knows how to use CF, then it can make the debate better. And if the debate isn't too adversarial, then people might be open to letting you translate some of their statements when you think it's important to.
My conclusion is that it's usually unnecessary to be picky about terminology, even when statements contradict CF, as long as you aren't discussing epistemology. CF is helpful to learn and use, but CF-contradicting ways of talking and thinking are still reasonably functional because they often make good approximations of CF-compatible statements. Even if CF is correct and the CF-contradicting statements contain logical errors, most of them can be translated to similar statements without logical errors, so the errors often aren't actually that big of a deal. CF offers improvements that are useful but not necessary most of the time. Also, since most people don't know CF, it's important for CF users to get good at translating statements from non-CF to CF terms. You can do that in your own head or in your notes when talking with people even if you don't ever share the translations with them, and use it as a way to understand what they're saying more precisely and check for errors (when translation is hard, be suspicious of their claim and investigate more).