(at around 11 mins) In the boat with Team Rocket, Brock's shirt sleeve changes from orange to green when Misty puts Togepi inside her knapsack.
Misty is shown with one set of Pokémon in one shot and with some entirely different ones in another.
In the mini movie, Pikachu's Vacation, when Pikachu is strolling along and the Pokemon run over Pikachu, Psyduck also runs on top of Pikachu, and runs off with the crowd. Then when the camera pans to the right, Psyduck is with Bulbasaur, Squirtle and Togepi.
After the real Charizard, Venusaur and Blastoise have battle cloned versions of other Charizard, Venusaur and Blastoise. Mewtwo "claims his prize" by capturing most of the pokemon (not his own, and some of the trainer pokemon are missed such as Misty's Togepi) so he can clone them which would result in 2 clones of Charizard, Venusaur and Blastoise (original and new) yet we only ever see the original clones.
In two very similar shots at the beginning and end of the movie, as Officer Jenny warns the Trainers about the storm, the backpacks of Corey and Fergus drastically shrink in size.
When Ash is trying to save Pikachu from one of Mewtwo's poke balls; he chews the metal arms that grab him. His teeth would have been broken.
If one listen carefully, one can hear Ash's original voice in the scene when he faces the second trainers' Pokemon.
When Fergus releases his Gyarados into the water to ride on its back, its lips are blue instead of yellow.
When Fergus runs over to his injured Gyarados, his Nidoqueen has the color scheme of a Nidoking.
Right before Ash charges at Mewtwo, one frame shows Rapidash without its flames. This was fixed in later releases.
When Ash rescues Pikachu from the clone machine, and Squirtle and Bulbasaur get released from their original poke-balls, Ash's English voice laughs, but his lips seem to be saying something, not "laughing"
When Ash receives the letter from Dragonite, we hear Togepi say "Togepi?" but its mouth doesn't move.
During the scene with Team Rocket disguised as vikings, Ash mentions Minnesota as part of a joke, which doesn't exist in the Pokemon universe.
When watching the Pokemon go through the cloning machine, Jessie and James call the silhouette of a Scyther an Alakazam.
At one point in the film, one of the trainers at Mewtwo's castle has a Pidgeot. He falsely refers to it as a Pidgeotto.
Fergus states that all his Pokemon are water types, however he has a Nidoqueen, which is actually Ground and Poison.
Meowth calls a Sandslash a Sandshrew.
In the opening credits battle sequence, Pikachu's Thunderbolt knocks out a Golem. Golem is a Rock and Ground type Pokemon, so it shouldn't be affected by electric attacks.