Conversation so far:
Is there anything special revealed about Andy's character in Season 3?
Early season episodes reveal his anger issues.
Does Andy have any rivals at work?
There is rivalry with Dwight Schrute over whether his title is higher.
Does Andy leave his job at any point in Season 3?
Andy's departure from subsequent episodes as due to being sent to anger management training.
When does Andy rejoin his job?
Andy returns a few months later.
Who else does Andy work with at his job?
Stanley Hudson.
Does Andy have any emotional problems at work?
Andy's mobile phone that rings with Andy's rendition of "Rockin' Robin" in the ceiling, enraging him into punching a hole in the office wall.
Is this the reason that Andy has to leave his job?
A producer's cut of the episode explains Andy's departure from subsequent episodes as due to being sent to anger management training.

Question: Does Andy get promoted at all during Season 3?
Self-contained rewrite: Does Andy get promoted at all during Season 3 of Andy Bernard?