"After the police found the money," Kovacs wanted more money to get out of town, so Denise killed him. But the police found the money on the dead Kovacs.
When Detective Briscoe and Logan find the pistol in the desk, Detective Logan sticks a pencil into the trigger guard and lifts the pistol out of the drawer. While used to demonstrate Logan's not wanting to get fingerprints on the weapon, there are a couple of serious flaws with that action. First, you would want photos of where the weapon was before it was ever moved. There is absolutely no reason to pick up the gun at this point. Second, and most important, is that the weapon may be loaded, and if the pencil depresses the trigger while being handled, it could discharge. No police officer, especially a seasoned Detective, would do either of these things.