Plot hole: When Prue first releases Matthew, he blinks several times, then blows out the windows and jumps out. Why would he do this and reveal who and what he is when he could have simply blinked? Obviously it was just a way to get the police involved so Andy could be chasing Prue through the episode.
Plot hole: Throughout the series, it's established that good witches don't freeze. In this episode, however, Little Piper freezes Future Prue and Piper when they come back to the manor to "kidnap" their younger selves. Simply because the Charmed Ones reason that only one "set" of sisters (past/future) could have their powers doesn't mean that Future Prue, Piper and Phoebe aren't good witches. In other time-travel episodes, the sisters remain immune to freezing and are still able to say spells make potions, meaning they are still good witches. For example, in Season 8 "Forever Charmed," Piper and Leo go back to 1975 (the same time-period as this episode) using Coop's ring, trying to find when Phoebe is alive again. However, when a startled Patty tries to freeze them, only Leo freezes. Piper does not, though she likely cannot use her freezing/exploding power in this time.
From Fear to Eternity - S1-E13
Plot hole: Prue finds an entry in the book of shadows about the fear demon written by her mother. How would her mother know anything about this demon when no one has seen him in nearly 1300 years, let alone how to defeat him?
Answer: That was a mistake in the series.
Also, the episode is called 'Babies First Demon' and this alone tells us that it's Wyatt's first time in the field (so to speak) and as the sisters say, they've done a good job of clearing up their own magical messes so far. Nobody really knows how advanced Wyatt's powers are, or will become. That's why the cleaners appear, to nip things in the bud. The Cleaners didn't want to chance that the sisters could clean Wyatt's magic up, just incase they couldn't. Therefore intervening themselves, just in case.