Coming from a program that did have a reputation for firing people I would say that the top 5 reasons for getting a pink slip are lies, more lies, lying, super-duper lying and mega lies.
I've often heard attendings say they can deal with ignorant, they can deal with lackluster technical skills but they cannot abide having someone they can't trust. Its not fun being an attending and wondering if the resident telling you that the patient is stable and you don't need to come in is being truthful. Of course, that assessment comes with experience but NEVER ever lie about whether you've done something or not...its much better to take the heat and admit you didn't.
I've heard of some programs firing residents for what amounts to poor ABSITE scores. Of course, programs aren't supposed to use the in-training exam scores to make decisions about resident advancement, but IMHO many do. However, they have to officially find another reason to fire you rather than exam scores, so things like lying, unprofessional behavior (being rude to co-workers, allied health care workers, patients and families), drug and alcohol abuse, "behavioral problems" (ie, not answering your pages, not showing up when you say you will, repeated tardiness, etc.) will all go into your file and make an appearance when it comes time to decide about the contracts for next year.
Its fairly hard to get fired for most decent residents, but as noted above, if you gain a reputation as a liar, a cheat, untrustworthy or just plain unpleasant, all eyes will be on you looking for a reason to fire you.
So:
1) if you forget to order a test, check on the results, know what the labs are, etc. - own up to it and fix it. Don't lie about it.
2) answer your G-D pages. Make sure when you're in the OR that someone else answers your pages. Not all pages are for minor things and sometimes important issues will go undealt with because the nurse keeps paging you (despite you not answering).
3) go see the patient - see your consults in due fashion (we had a 30 minute window in which to see ours); if you're going to be late, let the service requesting your consult know.
4) load the boat; when things start going downhill, let your Chief know. Most Chiefs will take the blame for something when it goes wrong...after all, they are responsible for at least some of your education. But if it gets found out that you never told them that you started your post-op AAA on a new drip, your arse is going down.
5) call your own consults; don't let the students call or the nurse. YOU are the best source of information for the consultant and its greatly appreciated.
6) when you order tests, know the results. If the results aren't back by evening rounds, know when they will be (the stat CT scan hasn't been done and its two hours after you ordered it? Call Rads...find out why and when its being done. Better yet, give them heads up about any stat orders.)
7) even when you are tired and hungry and sex-deprived, try to be as pleasant as possible. It goes a long way.