Out of Universe, the changes to the Turtles' costumes obviously stems from complaints about them following the first film, but there's probably a reason for it In Universe too: April. With a human friend on their side the turtles don't have to rely only on what they scavenge off the streets to clothe themselves, as now they have April to help hunt down or order size XXwhatever athletic wear for them.
To add to this, remember that in the first movie Splinter did not want them going to the surface, with him even punishing them for doing so. Here? He doesn't mind that they went to a basketball game and encourages them to stop the foot. Thus, while in the first film they had to be sneaky and probably got almost everything from the sewers, by the second film they can actually go and grab what they want. Considering that Donnie is able to order pizza and have it delivered, would it be a shock that the turtles have an Amazon account?
The Shredder losing his Powered Armor out of universe is obviously about the complaints from the first film, but in-universe, it was likely severely damaged from his fall in the last film before being confiscated by the police, and Eric Sacks was arrested and thus in no position to build him a new one.
Adding to this, it also might explain why the Foot Clan are ninjas instead of the militia they were in the first film. With Eric Sacks arrested, the Foot no longer have his resources to utilize. Their newfound ninja training may be result of both trying to get on even grounds against the skills of the turtles, but to also make up for their current lack of artillery.
The mutants display traits corresponding to their respective animal:
The Turtles use their aquatic skills to swim well in the water rapids in Brazil and to survive the waterfall drop afterwards.
Bebop is seen eating from an oil drum of spaghetti, in line with how pigs have large appetites. It’s a non-lethal and comedic version, but given that pigs can be seriously omnivorous (Guy Ritchie’s Snatch showcased a man feeding corpses to pigs), if Bebop had been really unleashed he could have had Turtle soup for dinner.
Splinter is a notable exception, as in most films he is able to fully maintain control of his humanity (even if he started as a rat first).
