What points should I tell to someone whom I'm encouraging to join MathOverflow for a better contribution to this site and avoiding problems of any type as much as possible?
As quid comments, reading the manual/FAQ/help documentation covers most things. Let me highlight some things from a certain perspective.
MathOverflow is a repository AND a community. The idea is not just to get help, but to build a corpus of good questions and answers, so that readers of the future can find useful information more quickly. Further, if online collaborations over small (in terms of writing) questions work well, they may result in larger collaborations on projects not suitable for a forum like MathOverflow where discussion takes a back seat to clarification and direct relevance. With this in mind, I recommend the following:
a) Pretend you are at an informal and otherwise professional seminar. If you don't understand because (say) something is poorly worded or constructed, respectfully ask the speaker, but if you don't understand because you are new to the subject, ask someone outside the seminar where to start. Think about what contribution your question or answer may make before submitting. Oh, and wear pants and talk nice. (Don't be a jerk at a seminar.)
b) Realize your contributions can be edited by others. The basic intent of all edits should be to improve clarity and quality, and if everyone plays nice, people only improve on your stuff.
c) If someone tells you that you are making a mistake, consider their point and whether they may be right. Acknowledgment may not be necessary, but ignoring is done at one's peril of losing the privilege to be a community member, especially if a moderator is recommending a change.
d) Ask for help, and do it the right way. Usually help on math questions is for MathOverflow, and help for how to behave on/use MathOverflow or meta.mathoverflow is for meta.mathoverflow.net. If you are confused, say so, and start on meta. People here are often willing to help those who have read and are attempting to follow the rules.
e) I did mention reading the guidelines before you post anything, right?
Gerhard "Come And Play With Us!" Paseman, 2015.09.19