When watching the episode in which angel is enlised into helping a "poor defenceless" actress who is being "stalked", you will notice he crashes through her sliding door to save her from her "attacker" thus entering her house without permission...
all though i did notice this and the information is correct from that view Angel could have been told by the actress that he was welcome to her house anytime or something like that which would allow him entry into the house (like what happened in the episode where Cordy's house was inhabited by the ghost mom and she didn't want Angel to enter but he did b/c she had told him that he was welcome into her house anytime (when she obtained one))
Actually, earlier in the episode the actress did say that Angel was welcome to visit her any time. It would be taking it a bit liberally to assume this was an invitation...but apparently, that's all that is required.
In the episode, Rebbecca says only "well, stop by" which may or may not be considered an "Invite" but the very next line, Angel specifically accepts it as one, as he says Thanks for the invitation.... clearly this was not a slip of him crashing through the window later. It was rather subtle, but definately not a mistake. However, speaking of uninvited enterances, there is one just 1 episode later nobody seemed to catch in Five by Five. The guy at the very beginning is in the hospital, not dead, it is technically still his apartment when Angel walks right in without an invitation to confront Faith.