I live in an area that was quite active early on in OSMs history. At the time, with the exception of some rather off yahoo imagery for some areas, the only may way to contribute was via generating GPS tracks and naturally that meant over- and under-runs in corners by 2 digit numbers of meters, wrong topology (roads merging in to the wrong one in a complicated junction for example) and in places where reception in general is not so good (forests etc) way off tracks, but the result was perfectly usable (actually the topology issues were and are far more annoying than anything else).
As I mentioned we had some coverage by yahoo imagery early on and in those areas we've spent the last couple of years cleaning up details (mainly buildings) that were added from that imagery but unluckily from a bad source, creating a lot of completely unnecessary work with no real benefit at the time.
As a consequence, getting back to answering the question. I believe the correct answer is that the required precision depends on the level of detail you want to add and as a corollary you shouldn't be adding detail where the available sources do not support that level of precision reasonably.
Example: if you only have consumer grade GPS and no imagery, I would restrict myself to roads and map POIs as nodes and not try to add buildings en masse.