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: At Norinaga castle, Kenshin walks towards the Lord and kneels down. The number of people around them change between shots. Also, the horse on the far right that started walking away is suddenly next to the soldier.
Continuity mistake: When the turtles jump over the table, the tablecloth suddenly becomes way shorter between shots. (00:04:01)
Continuity mistake: For his curtain call, Stuart Wilson acts in close-up like he's losing balance, body arched back. The impact looks all different in the wider angle. (01:22:50)
Revealing mistake: The Turtles give chase to Walker; Leo and Raph run across a roof, but the tiles are obviously fake; look at Raph's feet and you'll see one in particular bending like gum under the push. (01:21:00)
Audio problem: The Turtles reach Walker's chambers. Seeing that he's escaping, one of them yells "C'mon, Mikey!" but nobody's lips are moving. (01:20:50)
Continuity mistake: Leonardo ducks the cannon shot tucking his head inside the shell with the bandana going in front of his shoulder, but he emerges with the bandana on both sides of the neck later. (01:19:50)
Revealing mistake: It's even too obvious when the movie finale turns into a bit of a farce, but when Mitsu elbows the guards to free herself, it's obvious that she does no damage - the guards are wearing armor, even - and the extras don't do anything to 'sell' the hit. (01:20:20)
Continuity mistake: The goons with guns arrive at the castle, "There goes the neighbourhood", quips one of the heroes. In one shot Raphael sidesteps towards Michelangelo to reach his arm, in the reverse it's Mike and Don who are restraining Raph from charging. Same mistake happens a few seconds later, when Walker delivers his "Who's your tailor" line and Don is restraining Raph, or not. (01:17:35)
Revealing mistake: The rebels broke into the court of Lord Norinaga's palace. Donatello knocks down two guards with a leapfroggin' double flying kick. Which sounds way cooler than it looks, because it is obviously miles away from actually connecting. (01:15:15)
Continuity mistake: In the fight alongside Mitsu, Donatello beats up some soldiers by the table with the scrolls ("Bases loaded, home run"). The scroll is placed in a different, more orderly way than before (when it was on top of another parchment). It wouldn't tidy itself up during the fight. (01:13:40)
Continuity mistake: After learning about their supposed ancestors, the Turtles begin fighting Norinaga's guards. Michelangelo is the first one in their way and is at a standoff with one of them who has his sword raised, and still the following shot shows exactly Mike facing some enemies that run at him. (01:13:10)
Revealing mistake: The grate on the prison floor (left open and unguarded after they escaped from there the first time) is made of thick metal...or so it looks, because when Michelangelo climbs up, it wobbles by the lightest tap of his elbow. (01:09:55)
Revealing mistake: Walker celebrates the news that he's gonna get the agreed price on his shipment from Lord Norinaga. He fires his cannon, which not only must be firing a cluster projectile since it disintegrates in a single shot 3 targets, but also it makes them implode. (00:58:20)
Continuity mistake: Raphael points out that Yoshi is no 'senior citizen'. He adds "Come ooooonnn..." and in the passage from one angle to another Raph's bandana moved from the front to the back of his shoulder. (00:56:50)
Continuity mistake: Leonardo picks Yoshi up from the ground after reviving him; his bandana goes down his left shoulder, but in close-up goes down both sides of his neck. (00:48:30)
Audio problem: Michelangelo runs inside the burning hut yelling "Here I go!" with his mouth closed. (00:46:10)
Continuity mistake: In Niles' POV, during their first confrontation in the middle of the village raid Walker on his horse is in the shade, facing Michelangelo in sunlight. It's the opposite in their respective close-ups. (00:44:15)
Revealing mistake: In a complete non-sequitur, the Turtles declare that they are friends, taking off their masks. Mitsu picks Raphael's helmet up herself; not only her hands chance place on the helmet at the cut, but the helmet is soft rubber under her fingers. (00:40:25)
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."