When Hedorah throws some sludge at Godzilla during the Mt. Fuji scene, it hits Godzilla's right eye - but after Hedorah gets done laughing, Godzilla's left eye is the one that is damaged.
When Dr. Yano and Yukio are discussing going to rescue Ken, fish can be seen swimming in the aquarium behind them even though all the fish in it were destroyed by the acid mist a few minutes earlier.
When Godzilla flies after the smaller Hedorah, he appears way too small compared to his enemy.
When the child notices Godzilla from far away on the roller coaster ride, it is clear that "Godzilla" in this case is just a badly drawn blotch of paint, which also appears to be far too dark for its supposed environment.
The music ostensibly played on the guitar (and then by the band) in the field does not remotely match what the musicians' fingers are doing. It is not a case of lag, but that they are playing entirely different things.