Hi,
Shouldn't be any major problems. I travelled a couple of times within the US during both my training and working period. When it comes to leave the US for a visit home, vacation etc. it's not a problem to get in or out as long as you always bring your papers, to prove that you are following an education program (studying) and of course identification (passport+visa).
I have a friend travelling now soon with a J-1 and he was told that he could enter the US 1 month before start of visa and leave 1 month after expiration of visa.
i would strongly recommend you to check with the embassy to avoid any confusions. They now best what the rules are concerning enty&departure under the visa
they issued you.
good luck!
