As Harley performs Say We're Sweethearts Again, the piano player's legs vanish for one shot.
Joker had three henchmen in the biplane, two in the driver's seat area, and one in the tail gunner slot, yet at the closing only two of the henchmen are seen crawling out from the crashed burning biplane.
Joker tells Harley they'll get to a high altitude and watch the nuclear bomb go off on Gotham, but Joker using a biplane and the highest recorded altitude for a biplane was set in 1938 at 56,047 ft. That places the maximum altitude a biplane can reach at around ten miles up, and the fireball mushroom cloud of a nuclear bomb goes far beyond that height.
Dropping bombs from his biplane onto the grounds of Mayor Hill's mansion is a risky move on Joker's part, since that's where the nuke is.