Revealing mistake: In the scene where the turtles are leaving April's home and stop at the door to say hello before leaving, you can see Leonardo's sword handle bend like rubber, which it in fact is. (00:27:10)
Revealing mistake: A lot of times in the movie, when the turtles' mouths are wide open, you can see the cast. An example of this is the scene when Raphael wakes up in the bath tub and Leo hugs him. When Donatello tilts his head back and laughs you can see eyes, a nose, and a mouth within the mouth of the costume.
Visible crew/equipment: In the shot in April's apartment where Leonardo and Raphael are arguing about how they should look for Splinter and the Foot, a crew member with an orange hat can be seen ducking behind the table on the left. (00:38:00)
Visible crew/equipment: When Splinter throws Shredder over the wall, Splinter's puppeteer is visible. (Full screen only).
Visible crew/equipment: When Shredder is charging at Splinter with the spear the edge of the backdrop and a hanging wire are visible at the top of the screen. Full screen version.
Revealing mistake: When the Turtles make their triumphant entrance jumping in frame after the logo, at the bottom of the screen you can tell they are wearing white socks/shin guards, except Raphael who is the one the camera is focused on. (00:05:30)
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: 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: Two shots after introducing himself to Raphael, Casey Jones' hockey mask vanishes from its spot on the grass in the background (full screen version). (00:12:15)
Continuity mistake: After Master Tatsu kicks his opponent in the face, a couple of bystanders in the background instantly move further apart from each other between shots. In addition, one of them is a Foot member who loses his nunchaku as the shot changes. (00:32:30)
Continuity mistake: After decking Raphael for the Jose Canseco remark, Casey's baseball bat instantly changes hands between shots. (00:12:35)
Continuity mistake: As he shouts down to Michelangelo through the sidewalk grate, watch how the pizza man's $10 bill changes from left hand to right in between shots. (00:10:20)
Continuity mistake: In the beginning, after the Turtles save April, you see her jacket is on correctly as she sits up. A second later, it's off her shoulders. (00:04:25)
Continuity mistake: Right after Donatello busts through the barn doors with an old Ford truck, its hood closes by itself between shots. (00:53:10)
Continuity mistake: While driving Danny to school, Charles' left hand grips the steering wheel. But in the following shot where Danny opens the door to run away, his left hand is resting near the window sill instead. (00:30:25)
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.