Gina says that it's safe from Charles in the evidence locker because his scooter can't get up the steps. The area between the bullpen and the evidence locker has been shown many times and there are no steps.
When Doug Judy drives away, he pulls off the wire he was wearing and throws it out the car window. The wire is shown to be very short, maybe a foot or so in length. A listening device like that would typically use a longer cable and would have a received pack attached.
At 16:38 when they're entering to catch the Pontiac Bandit, the door clearly has a sign stating "PUSH" as the cop pulls the door open to let Jake & Rosa inside.
Despite the Pontiac Bandit's habit of stealing only Pontiacs, a Chevrolet Lumina APV (a rebadged version of the Pontiac Tran Sport) and a Dodge Viper both appear on the bulletin board profile of his transgressions.
Someone with a gunshot wound would have no reason to be wearing a cast, especially a cast that goes up so high.
Gina tells Amy to turn off her phone in the evidence room, even though Gina had already given one item of her preparedness checklist as having a fully charged phone. She ends up live-tweeting the entire experience, alerting Charles to their location. However, she could have meant that Amy should turn off the sound on her phone so that Charles couldn't hear them ringing.
Boyle's bandages/cast over his workout T-shirt would have no medical purpose.
After Jake finds a copy of An American Tail: Fievel Goes West (1991) in Doug Judy's spare bedroom, the two of them begin quoting, "Papa! and "Fievel!" That scene was from the original An American Tail (1986), not the sequel.