Continuity mistake: Often the show reuses footage of Clark Kent changing into Superman, but the footage has him removing his hat, even though before he rushes off to change he is usually not wearing a hat.
Audio problem: During the opening credits no one moves their mouth when they notice Superman and say "it's a bird...it's a plane..."
Other mistake: Superman is always seen with his arms extended when he flies, but when he lands, it's always feet first. He's never seen changing his position to account for this.