The toughest part of migrating from Server 2003 is getting started and maintaining momentum.
Sure there will be some technical issues that will drive you stark raving bonkers, but the biggest problem that most organizations face is getting started and staying on the migration track in a systematic way.
There will certainly be delays, even road blocks. People may leave. Budgeting estimates may be out of whack. Many organizations will allow this to derail them and there migration will splutter to a halt.
It is necessary to acknowledge that if the migration from Server 2003 to Server 2012 was going to be easy, someone would have done it a long time ago. Right now, time has pretty much run out. Just because the clock is running out though doesn’t mean that you shouldn’t start migrating. That’s because you’ll still have to do it at some point in the future and you don’t get to give up just because the migration deadline has expired.