When Buffy and Faith search for files in the Mayor's office, they enter the office, look around, and then leave, but not before spotting the Mayor and Mr. Trick. They head back into the room, waiting until the two black hats pass.
Later, we see the Mayor watching the security cameras. We see Buffy and Faith entering the office. After saying a few sentences, magically the tape is on the part where Buffy and Faith spot the Mayor and Trick...without fast-forwarding the tape at all.