Revealing mistake: When Raphael wakes up, and Donatello is laughing, when he opens his mouth, the actor's mouth inside the turtle's mouth. (00:56:25)
Continuity mistake: Just after the Turtles train by fighting with each other, Michelangelo is in the barn punching the punching bag. The very next shot is Raphael on top of the barn shouting out Splinter's name. Upon further inspection at the weapon at his side, this is not Raphael. It is Michelangelo. (00:56:45)
Revealing mistake: When three of the turtles are playing Trivial Pursuit and Leonardo runs in to announce Splinter is alive, you can see a wire coming out of Raphael's shell. I guess it's for the animatronic head, but it's visible. (00:59:30)
Other mistake: Danny (who somehow knows where the Turtles hideout is, maybe someone else in the Foot clan told him) is hiding in the closet, cowering in fear in a corner of it. April, who is way behind and with her view even further obstructed by Leo and the others as she steps to the left, guesses that it is him even if the little guy hasn't spoken a word yet. (01:03:45)
Continuity mistake: When Danny is admiring April's turtle sketches, he asks if he can keep one of them. His right hand holds onto a sketch of Leo at first, but in the following shot his right hand isn't gripping the sketch at all. Instead, he's seen reaching out to pick it up from the couch. (01:04:35)
Deliberate mistake: When Casey is hiding behind the boxes waiting to knock out a Foot soldier and steal his outfit, you can see he is still wearing his denim vest. After he knocks out the Foot soldier, he is able to put on his entire outfit in roughly three seconds. (01:10:15)
Visible crew/equipment: After Casey takes a golf club and drives Master Tatsu into a pile of boxes, a camera lens hood is visible on the left side of the screen. It can be seen again in a later shot right before Casey and Danny carry Splinter away (full screen version). (01:14:40 - 01:15:50)
Revealing mistake: In the scene close to the end when the turtles are fighting the foot soldiers on the fire escape (directly before the scene where Mikey ducks under the foot soldier's axe), Raphael thumps a foot soldier on top of his head and then rams the soldier's head into the stairwell. The only problem is the soldier's head misses the stair by about a mile. The sound effect of impact is there and the soldier even holds his head as if he were hurt. (01:17:20)
Revealing mistake: Michelangelo dodges the axe a Foot clan member swings at him by hiding his head into the shell. When he knocks his assailant out with a backhand, you can see a large gap between the mask and the rest of the suit. (01:17:30)
Continuity mistake: When the Turtles strike a pose after they wasted all the Foot soldiers before their big showdown with The Shredder, the ninja lie unconscious at their feet in different position. Even the roof is lit differently. (01:18:20)
Continuity mistake: Michelangelo and Donatello are standing side by each after Shredder introduces himself on the rooftop. But one shot later when Raphael steps in to take on Shredder, Donatello is now behind Michelangelo instead. (01:18:35)
Visible crew/equipment: When Leonardo takes his first turn attacking Shredder on the rooftop, you can see the raised platform that he leaps from, which gives the effect of a very high jump (full screen version). (01:18:55)
Audio problem: At the climax of the film when the Turtles are about to face Shredder for the first time, Raphael says, "I got him" and then runs to fight. When Raphael falls to the ground, his pair of Sai hit the ground but make no noise. There should be a metallic sound against the rooftop. (01:19:00)
Continuity mistake: The Turtles are making fun of The Shredder's name once he announced it. Look at Michelangelo when he recites the coleslaw joke; his bandanna goes down the right side of his back, but it's on the left side in the next shot. (01:19:05)
Visible crew/equipment: In the rooftop fight sequence with the turtles and Shredder, Raphael jumps over Shredder's head at one point and, here, you can see the crash pad that he lands on (full screen version). (01:20:05)
Continuity mistake: When Shredder unbalances Donatello in the fight his left foot is close but not inside the large shadow area, but Michelangelo attacks him right away and despite his lack of movement, now that foot is in the shadow cone. (01:20:20)
Revealing mistake: When Casey Jones gets off the garbage truck he rammed the fire escape stairs with, he punches two ninjas, but they go down (especially the first) before his fists connect (or rather don't connect). (01:21:10)
Continuity mistake: Near the end when the Turtles are fighting Shredder and Splinter makes his appearance, you can see Mikey starting towards Splinter only to be held back by Raph, then a few seconds later, when Leo rolls to the group, the scene happens again, Mikey heading towards Splinter with Raph pulling him back. (01:22:28)
Audio problem: In a close shot of Splinter holding Shredder's spear with Michelangelo's nunchaku on the building's ledge, Splinter's voice can be heard, but his mouth isn't even open (full screen version). (01:22:55)
Revealing mistake: After Splinter releases the nunchaku from Shredder's spear, he falls from the building's ledge. But notice how Shredder stops abruptly right before the series of shots which show him taking the long fall into a trash compactor, indicating that he actually lands on a mat. (01:23:00)
Answer: It's not really petty thievery. Shredder essentially has control over a large crime syndicate which is involved in pickpocketing, burglary, and highjacking. And that's just the gang itself. The Foot Clan itself is probably involved with other activities that we haven't seen.