A few slip ups!
In the episode prior to this one, Bad Girls, Faith stakes a human, thinking it was a vampire.
At the end of the episode Buffy goes to Faith's motel room the day after to speak to her about it.
The start of Consequences Buffy wakes up from a nightmare and goes to school. This means it is at least the second day since the murder.
However later in the episode you hear the detective questioning a witness and he says "You heard the man scream at about what time last night?"
When really it would have been two nights ago. Not the night before.
The detective asks the woman what time she head the man scream but if you look back to the episode Bad Girls, the man didn't scream.
When the police are investigating the dumpster which he was stabbed against, you can see blood at the top of the dumpster, smearing down to the bottom but when Faith stabbed him in Bad Girls, she didn't stab him until he was already on the ground.