In the episode "Dear Boy" Kate and a group of cops storm into Angel's hotel to arrest him. When she finds that he isn't there, she orders a couple of officers to be posted outside the building in case he comes back. Near the end of the episode (the next night) there is a shot of the outside of the hotel - you can clearly see Angel's car parked outside and in the next shot he is shown sitting in his room.

How did he get in?

If Kate was so intent on catching him, would she only post officers there for one night? If they were there, how could they not notice the very man they were meant to be watching for pull up in a large black convertible and stroll in the front door?