The "state of the art digitized deck" they use to view the security tape from the hotel only has a power cable plugged into it, no cable to connect it to the TV.
In the first scene we hear a band with horns, featuring trumpet, but the shot of the band shows only a rhythm section and one saxophone.
The detectives ask an officer to dust an entire hotel room for prints. Then they immediately start grabbing door knobs without gloves on and opening doors.