It's only natural to assume that things right after a breakup aren't going to be easy, and chances are you won't be in the best frame of mind to make all the delicate decisions that can shape your chances of success in rebuilding the relationship and getting your ex back...so everyone makes mistakes. What you need to do is make sure you don't make the WRONG mistakes.
The two deadliest mistakes that can also be avoided relatively easily stem from breakdowns in communication...namely, saying things to your ex you really shouldn't be, at times where contact really isn't the best idea. The two poster children of this category of breakup breakdowns? Text Message Terrorism and Drunk Dialing.
1) Text Message Terrorism: at its simplest form, TMT is a bunch of phone calls or text messages. At that basic of a level, it may not sound too bad...but when you actually factor in just how MANY phone calls or messages we're talking about, you can see that it's really quite the storm and can really mess things up between you. Even if it's for the best of reasons, sending message after message to your ex will only end up making things more tense and frail between the two of you.
2) Drunk Dialing: Less concerned with quantity, and more with the quality of one particular call or message. Generally it happens late at night, after you've had a few drinks and are feeling really lonely and emotional. As you can imagine, you pour your soul into your ex's ear, and it makes you look weak, desperate, and like someone he's glad to have separated from.
Both of these mistakes are devastating if left unchecked, but if caught and countered or avoided completely to begin with, they can be recovered from or stopped from ever giving you any trouble. You just have to see them coming, or see that you're doing them...and see them for what they are.