When Angel and Faith meet with Mayor Wilkins, the Mayor tells Angel not to kill Buffy too fast as he doesn't want a new Slayer popping up anytime soon. Even if Buffy is killed there wouldn't be a new Slayer to take her place. Kendra was her replacement after the master killed her in the first season. Then when Kendra died at the hand of Drusilla, Faith was called. So the only way another Slayer can be called is if Faith dies. This isn't necessarily true. Having two active Slayers is unprecedented. The only way to test it is to actually kill Buffy again. The Mayor (or anyone else) couldn't be sure and he doesn't want to take the chance.
When Faith comes to Angel the first time, she shows him her hands covered in blood, but when she touches Angel's neck and hair, and her own hair, and even rubs both hands across Angel's shoulders and neck, she leaves no trace of blood behind; her hands are clean. In fact, the blood on her hands is shown to be dry and it would be obvious to assume that in the time taken for her to get from the demon's house to Angel's mansion that this would be the case. Therefore, there would be no blood transfer onto either Faith or Angel.
When Buffy and Faith go to the demon's apartment, you can see where the front door's jamb was broken away when Faith kicked it in on her earlier visit, but when Buffy closes the door you hear the latch engaging an intact jamb with a strike plate, which we just saw is no longer there. The same goof occurs when Faith pulls the door shut as they leave.
When Mayor Wilkins is stabbed through the hand after Angel throws him the letter opener, the retractable blade of the prop knife is briefly visible as the Mayor retrieves it from the wound.
As Buffy looks down at the slain demon, she remarks "This wasn't just a hit. It's somebody's idea of a party." By the way she shakes her head as she looks down aghast at the carcass, everything suggests a blood-soaked crime scene. Yet when Faith had killed the demon, it was clearly shown to have been done with a single stab.
There is no actual need to let Faith flee after playing her, especially since Giles was in on the ploy. Instead of revealing it all to Faith like bad Bond villains, they could have captured her at minimal risk.