After Piper says "Fine, be that way." and Paige says "Fine, I will." We see Paige go back to and sit on her seat. When we pan back to Piper's face we see Paige about to sit on the chair again.
(at around 34 mins) The real seal of the Department of Homeland Security looks much more complex and sophisticated.
When Dex drops Phoebe in the front hall, the shot of him pulling her back up clearly reveals a stunt woman in a black wig.
After Leo comes into Piper's room with Chris and asks for the baby Tylenol, you can see that the mirror on the right that Piper and Paige were looking into is actually painted green.
Phoebe tells Billie that the detective "must have known you are connected to us somehow." He just followed Billie to the Halliwell manor, so that would be the very obvious somehow.