During the junkyard scene, just before Donatello is thrown, you can clearly see that Leonardo's katanas are in their sheaths. After he is thrown the shot cuts back to Leonardo fighting and his katanas are no longer there.
While Tokka and Rahzar are causing damage to the neighborhood after Shredder released them, the neighborhood lights stayed on even though they tear down power lines in the street.
When Shredder becomes Super Shredder, his costume somehow has more spikes on it. Also, his clothes are not torn from growing to massive size.
In the junkyard scene, part of Marc Caso's arm can be seen when Leonardo reaches for his katana blades and his costume opens up at the elbow.
In the first fight scene, Keno does a sweep on one of the bad guys, Keno clearly misses but he still falls to the floor.
Wires can be seen coming out of Leonardo's shell at the beginning when they are all eating pizza with April.
When Keno is running from The Foot's Soldiers in the junkyard aka. The Foot's HQ, you see him fighting against two of The Foots soldiers, and another guy running in the back, ready to do jump over the junk in front of him, and do a saltomortale. Before the saltomortale, he jumps up into the air, like he is about to jump onto a trampoline.
Before the final fight with Tokka and Rahzar, when Donatello and Professor Perry deduce that they need CO2 in order to destabilize the mutation, they find a fire extinguisher. When they grab it, you can see from the pressure gauge that it is in fact not a CO2 extinguisher. This would make sense because CO2 extinguishers are primarily used for closed in areas or electrical equipment.
The turtles moving into the abandoned Subway platform is guaranteed way to soon be discovered by the NYC power company investigating an unpaid power drain on the city from the massive amounts of electricity it takes to power a subway platform.
In the club, as Michaelangelo and Donatello are fiddling with the musical instruments, we see Donatello turn the amplifier to full and say, "Full volume" in Michaelangelo's voice.
At about 37:58 when Shredder tells Tatsu to remove the bar because "it's time they learned who their master is", the shot goes back to show Tatsu from the front, where his lips are clearly moving, but there is no sound.
At about the 52:47 mark after Donatello is thrown through the roof and rips the tape off of the TGRI guys mouth he exclaims "I gotta get the hang of that" to which the TGRI guy says "That's okay." immediately after "That's okay" you can hear someone on the set say "Teenage Mutant Ninja Turtles 107" in the background. Use headphones if you must.
In the first fight scene, when the turtles come down the stairs behind Keno, they come to a stop. Before they jump into the air for the title screen, you can see them jump onto what is assumed to be a trampoline.
During the fight in the TGRI lab with the Foot you can clearly see a mat in the background as one of the Foot Ninja lands in the background.
When Keno is waiting outside for the Foot audition, a certain part of Manhattan is visible in the background, however, when he is walking into the building, the background shows that he is at least a mile away.
When Splinter showed the Turtles the canister that had the ooze that mutated them, it says TGRI on it. But in the flashback of the first movie, the canister that spilled the ooze the Turtles were exposed to said Radioactive Material.
Tutso asks Shredder, "We rebuild the foot?" Shredder specifically says, "No." (because the only one thing that is next is revenge.) Later, Keno tells the Turtles that he's heard of the foot, because the word is out on the street that they are looking for anybody with martial arts talent, especially teenagers. That means they are recruiting people to join the foot, thus meaning that they are rebuilding the foot clan, even after the shredder said that there was no need to do so.
When the fight bursts into the club where Vanilla Ice is performing, it's clear that nobody in there has ever seen any of these creatures before, but in less than a minute, Ice and his band suddenly have a whole song ready, complete with lyrics and choreography.
How did Splinter knew that the Turtles were at the junkyard? Also, where did he get the bow and arrow from?
At the end of the movie Splinter refineries Vanilla ice's "Ninja Rap" song despite not having been in the club to hear him perform it.
Leonardo never thought of using his sword to cut the net that he, Donatello and Michelangelo were caught in.