Turn off display_errors, turn on log_errors, set error_reporting to -1 and look out for E_STRICT and E_DEPRECATED warnings.
This migration script (shameless plug) can help you with some of the deprecated things. It says 5.2 to 5.3 but may be useful for migrating from 4 too. And you can extend it (patches welcome :) for things you discover are frequently encountered.
PHPStorm IDE has pretty decent code analyzer which could point out some of the potential problems in your code. Give it a run through your app and see if it has something interesting to say. Also it will probably help you to find quickly the errors that may follow from using new keywords as function names, etc.
For your last question: IMHO you should go with 5.3, doing the job twice makes little sense.
