When Faith is shown sitting on the windowsill, the piece of broken, bloodied glass she eventually drops to the alley below changes from a triangular shape to the initial dagger shape she used on Wesley.
When Faith is torturing Wesley, Angel comes crashing through the door. He was never invited in and the man who owned the apartment was in the hospital, not dead. Angel never went to the hospital, Cordelia just told him where the apartment was. However, Cordelia said they should go talk to him. It's reasonable to assume they did go and ask for an invitation.
In the final fight scene between Angel and Faith, Angel is thrown against a brick wall in the apartment, however when he hits the wall, you can see the wall move near the top away from the ceiling.
When Cordelia and Wesley first try to enter her apartment, phantom Dennis forces the door shut a couple times, attempting to protect them from Faith, who is already in the apartment. However, after they do enter and Faith attacks them, phantom Dennis makes no effort to stop her.
At 37:41, Angel breaks down the door and enters the apartment without permission from the inhabit as required for a vampire to enter a private residence.