Continuity mistake: Kenshin loses his sword battling with the guards at the beginning of the movie. The sword gets stuck almost horizontally in a tree stump. Then one of the guards grabs it as he rides by with his horse, but the katana is now stuck in the tree at a sharper angle which makes it possible to reach for it and grab it on the fly. (00:02:35)
Continuity mistake: When the turtles jump over the table, the tablecloth suddenly becomes way shorter between shots. (00:04:01)
Continuity mistake: During the introduction of the turtles, Michaelangelo's bandana goes from the back of the shoulder to the front and then both ends behind the shoulders between shots. (00:04:30)
Other mistake: When April O'Neil arrives bringing gifts, she leaves the manhole cover completely open - there's also an awful lot of light coming from there, as if the abandoned subway station were built inches away from the surface. (00:05:20)
Continuity mistake: We first see Lord Norinaga in a close-up looking at his son's arrival. His helmet is tied under his chin, but when he walks in the helmet's cord is split above and below the chin. (00:07:40)
Continuity mistake: Walker's henchmen dump on the court Lord Norinaga's sentinels and walk away. They are already shown posing with evil smirks and all that in the next shot while Walker is doing his threatening speech. (00:08:55)
Continuity mistake: The pattern of the fabric below the sceptre changes between the first and second shot. (00:09:41 - 00:10:07)
Continuity mistake: When the scroll falls downwards, it is smooth, but from the immediate next angle it's got a big wrinkle. (00:09:54)
Continuity mistake: Kenshin throws a temper tantrum in a room with several statues. The doors open and a strong wind blows; the position of the scrolls on the table changes between shots; they are first closed by the edge of the table, then unfurl from a position much further behind. (00:10:10)
Continuity mistake: Leonardo shouts "He's a man!" when Kenshin appears in the Turtles' hideout; he is holding in the foreground with the right hand his book about katanas, but in the next shot it's on the table, under his left hand. (00:11:35)
Continuity mistake: April materializes in the same spot as Kenshin; her headset is placed away from the collar of the kimono. She is still in the same position when she spots the priest, but the collar is underneath the headphones now. (00:11:50)
Continuity mistake: In the sequence set in present time when the Turtles interact with Kenshin, once he faints seeing the giant Japanese-speaking rat the shopping bags on the table changed position - the blue bag the wind knocked on the floor is back, and the red bag is up and not horizontal. (00:12:00)
Continuity mistake: April's walkman is very conveniently prone to play randomly. She puts it down on the floor, but it is, together with the headphones, positioned differently practically at every shot in particular when the guards start bashing it and everything is closer together in close-up than in wider angles. (00:15:30)
Audio problem: April's walkman keeps playing for a while spreading in the air the suave notes of The Barrio Boyzz's "Conga" even when the batteries already came out on the first strike. (00:15:40)
Continuity mistake: Walker witnesses the music playing and the guards wrecking the demonic machine; he constantly has his left hand held up in the air in the close-ups, but in the other angle he shifted that hand to lean against the door. (00:15:45)
Character mistake: Pretending to be a witch, April says that the song the walkman played was obtained because "I shrunk four incredibly cool guys and I locked them in there." The Barrio Boyzz were five at the song's release. Did she let one Barrio boy go? Was one of the Barrio Boyzz uncool? (00:16:40)
Character mistake: Donatello is running a rather verbose program analyzing the scepter. On screen the text mentions the "time-space CONTINIUM" rather than "continuum." (00:17:45)
Revealing mistake: The Turtles are preparing their time travel. Splinter tells them "The scepter will be in the temple, which means..." Pay close attention here, because now the rest of the sentence is obtained dubbing the line over a rewind of the previous footage. (00:21:50)
Audio problem: Battling the Norinaga soldiers in the castle, Donatello parries several katana strokes using his wooden bo, which causes sharp metallic sounds every time. (00:22:50)
Continuity mistake: When ninja-Michelangelo is on the horse, the sceptre swaps hands between shots. (00:25:05)
Answer: Michelangelo wants to stay behind for the same reasons as Raphael: because in that time and place, they are well respected, even revered as heroes. They can live openly and not be banished to sewers or subway stations.
LorgSkyegon
Mikey didn't want to stay behind because of Yoshi but because of Mitsu. Raphael even points out that she's the reason he doesn't want to return. When Mikey says they should stay, Raph responds, "Now, forget about Mitsu and give me the scepter."