When Cher tries to get Fran to guess who she is, she says that she's won a Grammy, an Emmy, and an Oscar. However, in real life, at the time of this episode's airing, Cher had only won an Oscar. She would later win a Grammy in 2000, and an Emmy in 2003.
After Val tells her priest about Cher staying at the mansion, Fran asks if he was wearing his collar, claiming that if they aren't wearing their collar "it like having their fingers crossed". The Seal of the Confessional, which protects confessions, doesn't require wearing the collar (indeed, priests aren't ever required to wear one). As long as the penitent intends to make a confession, it is automatically confidential and can never be revealed to anyone under any circumstances.
The first time the press are seen from the outside, you can clearly see C.C. in front of the door facing the door. In the next shot, we see Max, then Niles enter the mansion from the outside view (C.C. no where in sight) , then you see C.C. hanging on the door when Niles opens it.