Continuity mistake: When Team Rocket takes off in the boat, it sinks. Their pokeballs float away, and Jessie says "Arbok and Lickitung are floating away!" But she doesn't catch Lickitung until Princess versus Princess (Season 1, Episode 52).
Continuity mistake: When the capsule containing the three pokeballs first opens up, you can see the names of the Pokemon etched into the balls (in Japanese). But when Ash picks them up, the names are gone.