When Eddie (John Cameron Mitchell) tells Lennie his rate (a-hundred-and-a-half, plus the room), from behind Lennie sits up and reaches into his coat. Switch to scene from in front of Lennie and his hands are still on the table for a second, then he sits up and reaches into his coat again.
Upon finding a raincoat the suspect had been wearing, Detective Briscoe first picks it up without wearing gloves, then pulls a gun out of the pocket again without wearing gloves. This would destroy any forensic evidence on the items.