At the end of "I've Got to Find My Baby" the drummer is seen to throw his drumsticks. Immediately after he is seen coming around his drum kit with a stick in his left hand, and immediately after that his hands are empty again.
When Elvis walks back Shelley from the 'Do the Clam' dance on the beach, she is barefoot (and not carrying anything); next scene shot is of them coming into the hotel pool area, she's back to wearing her white high heeled shoes (she had them before starting the 'Clam' dance on the sand).
Near the start of the movie the boys smear cream over a picture of a girl in a bikini. The cream changes places in the next shot.
When Shelley Fabares is reading a green book by the pool, the book has what look like wet fingermarks on it in some shots and not in others.
When Elvis is on the beach playing the intro to "Do the Clam," the sound is clearly from an electric guitar, but when Elvis is shown playing the guitar, it's a regular acoustic guitar, which sounds nothing like an electric.
When Elvis is playing the bass guitar (club scene right before the brawl) he sets the bass down, but you can hear the bass riff continue to play.