After Captain America stops two thugs from mugging an old lady, one takes off on foot, right in front of the other one who takes off in a dune buggy. The thug on foot runs in front of the dun buggy just as the dune buggy takes off, but in the next shot of the dune buggy speeding off, the thug on foot has disappeared.
Reb Brown and his stunt double have noticeably different physiques; the double's chest is much more defined.
The scene right after when Captain America throws the thug off the buggy, it shows a close up of part of his hand, not with a glove on. The next scene, his glove is back on.
Throughout the scene when Steve is helping Pete with his chores (feeding the horses), there is a microphone unit visible stuffed in the back of Pete's pants.