It was very hot out and the A/C in the office wasn't working. He opened the door and the window to create a cross-breeze. This allowed Eddie Kane to enter without the key.

If you stop and think about it, Riley Greenleaf was done in by a broken a/c. The broken a/c led to the open door. The open door led to Kane leaving a key that didn't fit any locks on the carpet. Columbo used that key as one of his traps for Greenleaf.

Or, Eddie Kane tampered with the AC at some point?