Continuity mistake: In one of the first shots at the Freedom Day celebration in front of the Lincoln Memorial, we see a banner, with the text "Freedom Day - Express yourself. I hate my job.", suspended between to poles. Some of the banner can also be seen during the first part of Nixon's speech. But when it gets time to lower "Old Freebie" (the flag) the banner has disappeared and the flag is lowered into the position where the banner hung before. And the banner was tied to the two poles so they can't have raised it.
Continuity mistake: On board the Nimbus where Zapp asks for the activation codes for the global defense network, it immediately after cuts to a shot of Kif Saying "Aye Aye sir". In the background of the shot sit two ship crew members, the brown haired one on the left disappears in the following shot.