Also, if the judgment reflects the first date, is that a valid judgment or does that judgment need to be corrected?

When the defendant voluntarily absents himself, the court can continue on with the punishment hearing, hear all evidence, and determine a sentence. What it can't do is formally pronounce the sentence without the defendant there. Whenever the defendant is taken back into custody, he should be brought before the court and formally sentenced to the pre-determined sentence. The judgment should reflect the formal sentencing date, and you can nunc it if it doesn't.