During the scene at the amusement park in the "Amazing Journey" sequence, young Tommy can clearly be seen laughing while seated on one of the whirling rides. This is incorrect, as Tommy is supposed to be completely unresponsive to his surroundings.
In the "Pinball Wizard" scene, the Who's John Entwistle starts the scene playing a Gibson Flying V bass, and ends it playing a Gibson Thunderbird with a Fender Precision neck (a "Fender-bird"). He also starts the scene with long sideburns, and seems to finish it with a fully-grown beard.
In the "Pinball Wizard" scene the "Pinball Wizard" (Elton John) pulls the handle to launch the pinball on his machine. The ball is then lost when it goes below the paddles. During the rest of the scene there is a ball in the machine even though Elton John doesn't pull the handle to launch a ball again.
During the climactic "Listening to You" where Roger (Tommy) is running and crawling through water (clearly soaked), the camera shot changes to meet Tommy as he emerges over the top of the mountain completely dry.
During Ann-Margaret's "Rain Champagne" scene, the bottle of champagne she is 'drinking' from is clearly empty-several times in the scene it is lying on it side on the floor yet nothing flows from it, and during the close-ups where she is supposed to be drinking from the bottle, you can see that there is nothing inside it.