Continuity mistake: At the end of the "Food Food Food" song, Popeye gives Wimpy the hamburger, and starts a conversation. There are two ketchup bottles on Wimpy's left. At the beginning of the chat, both bottles are nearly empty with just about a 1/2 inch in both. As the shots progress, the one nearest Wimpy goes from nearly empty to completely full and back again several times.
Other mistake: As the people are going up the ramp to the Oyl's party, the man in the brown stops by the piling with a paper. As he bends over, there is a sound of the pelican pooping, and the man reacting to poop on his paper. The man and his paper are on one side of the piling, and the bird's tail is on the other. Couldn't have pooped on the paper unless he threw it.
Revealing mistake: At the end, in the fight with Bluto, Popeye was facing him on one side, goes underwater, and pops up on the other side. If you watch closely, the figure that goes under is the stunt double, as nobody can get from one spot to another about 15 to 20 feet away underwater in the space of three seconds. Also before Popeye comes up, you can see him underwater as the other figure goes under.
Continuity mistake: At the Oyls' house, during the engagement party, Nana Oyl gives Bluto a cup of tea, and moves off across the room. A few moments later after he drinks the tea, he starts to eat the teacup, and we see Nana's hands in frame on the right side where she served from. In the next shot, she's all the way across the room, too quickly.
Audio problem: At the beginning of the fight at Rough House's, after Popeye says "Enough is enough", it looks like he elbows the two nearest guys. If you look closely, they react a split second before the elbows get them, and the sound completes the illusion. Also, the last guy Popeye is punching in the face is moving just out of sync with the punches. The sound is like a punching bag, but his head is recoiling just a split second out of time.