As Micky Dolenz is climbing up onto the tank, the main gun is locked down in its rest. In the next shot, as he climbs the last bit and enters the hatch, it is unlocked from the rest and raised into battery.
When Micky Dolenz jumps from the bridge at the start of the film, the replacement dummy enters the water head first. In the next shot, when we see the real Micky entering the water as seen from below, he enters feet first.
When the cop orders The Monkees out of the box, he is wearing sunglasses. The camera angle changes as they climb down, and suddenly the sunglasses are in the cop's hand.
In Frank Zappa's scene, Davy Jones's left arm changes from being by his side to being on the cow's back between shots.
When Michael Nesmith is on the bridge in the opening sequence, his sunglasses disappear and reappear between shots; then his jacket disappears.
Flipped shot: when Micky Dolenz, Davy Jones, and Michael Nesmith are cornered by the man in the cloak, the part in Mike's hair is backwards.
As Micky Dolenz is sliding down the vacuum cleaner inlet, Peter Tork's shadow can be seen at the top of the slide as he moves into position.
As the Black Sheik rides across the desert sand, hoof prints from earlier takes are seen.
Wires pulling the mermaids and Micky Dolenz through the water can be seen at the beginning of the film. Wires are also visible supporting The Monkees before getting sucked into the vacuum cleaner, and when falling from the sky onto the street at the end of the film.
Annette Funicello's character is called Theresa by Davy Jones before the boxing sequence, but is listed as Minnie in the end credits.
The Italian flag decal on the tank is backwards - red/white/green instead of green/white/red. This may be a flipped shot, or alternately a gag.