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.
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)
Visible crew/equipment: At the end where all of the turtles are complimenting themselves, Splinter's puppeteer is visible when he walks onscreen to say "Cowabunga" (full screen version). (01:27:00)
Visible crew/equipment: As April walks from the bathroom trying to get Charles off her case, the top of a camera operator's head is briefly reflected in a mirror above the aquarium. (00:29:50)
Visible crew/equipment: Just before the ceiling collapses on the antique store a boom operator can be seen on the right hand side of the screen.
Visible crew/equipment: When Michelangelo retracts his head from a sword blow into his shell, you can see a crewman's hands under his armpits, holding and moving his upper arms.
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)
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)
Answer: Most likely to kill Shredder and make sure that there would be no way to come back but, as seen in the sequel, Shredder does return.