Citing low quality papers (solutions) in surveys? I sometimes find papers that aim to solve the same problem that I am working on, but these papers are of terrible quality. Some of these papers: 


introduce wrong solutions, 
re-introduce a solution that is already published, or 
are just very hard to understand because of the low quality of writing. 


Should I cite these papers in my "related work" section when writing a paper?

Would it be offensive to tackle these papers and prove that they are wrong (especially as the most of these papers are published in not very good conferences)? 

Or is it perhaps a waste of time to pay any attention to these papers?
Speaking from the perspective of a no-longer-quite-so-young mathematician, this is a serious question. I think one should acknowledge "prior art", even if one disagrees with many aspects of it. That is, to pretend that something doesn't exist when one is aware of it is dishonest. (I do not think that one's bibliography must only include things one has used... that can be subverted to argue, as I have heard a distinguished mathematician say, that one need not cite anyone else's work _if_one_is_careful_not_to_look_at_it_.)

Yes, there is the awkward issue of giving an opinion on "prior art" that one finds deficient. As @Shion comments to the question, one probably should hesitate before being too sure. The universal non-commital (therefore slightly dismissive, which is the right amount) comment is something like (at the end of introduction) "Compare [A], [B], [C]." Not saying that they're crap, or failures, or anything else. Just admitting one is aware of them, and pointedly not endorsing them... if that's one's intent.

That is, I think that published papers should not just be update-reports, but have sufficient scholarly context-setting to orient a genuinely interested reader not already completely expert, for example. I realize that the literal function of many "published papers" is merely "making a living", but it is not profoundly difficult to do somewhat better.