How and when to consider 面子 when speaking Chinese?
A mistake I make often (but sometimes it's kind of fun) is connecting peoples names to bad things.

Like:

A: 我姓刁。

B: 哦，是刁难的刁，对吧？

People seem to be kind of offended by this kind of stuff. Try not to connect it to 'bad' or 'negative' 'non-positive' things.

edit: oh yeah - also don't use 以小人之心，度君子之腹 with people [that is including the person you are talking to into the saying] even if you think it's a perfect fit for the situation - people will just assume you are calling them a 小人...