I've came across an interesting page on Wiktionary about Polish defective verbs
I get some of them like "powinienem" and "można", but I'm just curious about the usage of the other ones. Why would it be better to say "Trzeba ci wiedzieć" instead of "Potrzebujesz wiedzieć" , for example? Or "Należy wiedzieć" instead of "Musisz wiedzieć"?
I think most of the time those words are used in a not personal way. It is a bit like impersonal "się" you asked about. Trzeba wiedzieć= one should know. należy wiedzieć-one should know.
"Trzeba ci wiedzieć" seems mixed registers to me. Trzeba wam wiedzieć sounds like a part of a speech.
The difference is quite subtle - I am not sure what the grammatically-linguistic difference is, but this is based on how it sounds to me (as a native speaker):
"Trzeba ci wiedzieć" vs "Potrzebujesz wiedzieć" The first phrase sounds a bit humorous due to its old-fashioned structure, with an emphasis placed on whatever comes in the secondary clause. The second phrase is less emphatic and just shows necessity of certain knowledge. You need to know this for whatever reasons. "Trzeba ci wiedzieć, że mam obsesję na punkcie czekolady" - "You ought to know that I'm obsessed about chocolate" [e.g. because we're about to go to a chocolate shop and I'm warning you that I might go crazy]. "Zanim pójdziesz na bankiet, potrzebujesz wiedzieć jak rozróżnić widelec do mięsa i do ryb" - "Before you go to the banquet, you need to know how to differentiate the knife and fish forks" [e.g. because without this knowledge you will not be allowed inside].
"Należy wiedzieć" vs "Musisz wiedzieć" Here the difference is simple. "Należy" is "ought to" or "should", plus the structure is impersonal. "Musisz" means "you must", and is more direct and also more imperative, showing that there is less choice you have about the subject. "Należy wiedzieć, jak funkcjonuje system głosowania" - "One ought to know how the voting system works" [e.g. because it is a sign of sophistication]. "Musisz wiedzieć jak użyć gaśnicy" - "You have to know how to operate a fire extinguisher" [e.g. because otherwise you won't be allowed to work].
Not a native speaker, but I suspect the difference is that potrzebować can only be used with nouns. In general, it seems like Polish does not use the modal+infinitive construction as often as English, and only certain verbs can be modal. Native speakers are always correcting me for misusing them. The last lesson in the tree is about a way of turning verbs into nouns where we would often use an infinitive construction in English. So należy and trzeba are probably needed when you want to use an infinitive (i.e. wiedzieć). I'm not sure how they compare to musieć, which is a modal verb.
Somebody please correct me if I am wrong!