Plot hole: When Gith takes the potion from Chris, he ends up stomping on it and shattering the potion bottle - making contact with the potion. We've seen that potions don't have to be thrown by someone who's even a witch for them to work (like when Cole's powers were stripped etc) so why on earth would he do this? And how did it not vanquish him? There are other ways he could have gotten rid of the potion that didn't involve a way that really should have vanquished him.
Plot hole: In the opening scene, Chris directs Piper and Phoebe on how to vanquish the amorphous demon. He says that it will attack "fast and hard" as soon as it senses Phoebe's magic when she levitates. But Chris had orbed out of the warehouse and back in, and the demon didn't react to the magic. Later in the episode, it is specifically attracted to a use of orbing, several times.
Plot hole: This episode takes place in 1967, and Penny (Grams) is married to a man named Allen Halliwell who dies in the episode. Allen is supposed to be Penny's "first husband," Patty's father and the Charmed Ones' grandfather. But it was previously established that Patty's father was named Jack, and he died in 1964. Also they hint that Patty is still little but we know she was born in 1950 so she would be 17.
Plot hole: Rick is menacing Phoebe with a gun near the end of the episode. Why doesn't Paige orb the gun away from him? In fact, why did Phoebe make Piper stay upstairs? Piper could have frozen Rick, and Paige could have orbed him back to the prison. There were several obvious ways to resolve this situation that would not have caused Rick's death.
Plot hole: It's shown with the spell that the Halliwells leave for Chris in the attic that if something happens in the past, the future will immediately reflect that change. Chris had changed so much in the past that there should have been at least one thing different that mildly surprised him, even if he was careful to not give too much information to the sisters about the future.
Continuity mistake: The Stillman sisters strip the Charmed Ones' powers by using the same spell as Aunt Gail did in Season 2 (How to Make a Quilt out of Americans). But in that episode the Charmed Ones had to first drink a potion and Aunt Gail needed to wait a certain amount of time (at least 30 minutes) before the spell worked. In The Power of Three Blondes, the Charmed Ones never drank a potion and lost their powers before the Stillman sisters even finished the spell.
Other mistake: In previous episodes it is stated that good witches don't freeze. But after Piper has been decapitated and her head is placed in the manor, one of the students freezes all the kids by tapping into Piper's freezing power. The kids are all good witches so they should not have frozen.
Other mistake: Paige's spell causes Darryl to acquire invulnerability and uncontrollable super strength. When he opens the door of the squad car, he accidentally rips it completely off. When he tries to put the suspect into the back seat, the man flies through the car and barrels out the other side, taking the other door with him. But immediately before this, Darryl high-fives several of his fellow officers, and they are unharmed. They should have been thrown off their feet and suffered multiple fractures in their hands.
Continuity mistake: During the scene when Paige goes to the citrus plant during the labor rally, her pink blouse is quite short, baring her entire midriff. When the security guard throws Paige out of the plant, Rose McGowan's stunt double is wearing a shirt in the same pink color, but it reaches all the way down to her waistline.
Plot hole: Paige sees Margo leading the labor rally at the citrus factory, and then is stopped by a security guard. In the next scene, Margo and her sisters are entering the manor, and then after that Paige is thrown out of the factory. But how did Margo get from the factory to the manor before Paige was thrown out, when she was in the middle of the rally?
Continuity mistake: Robin falls over backwards after Paige dumps a cannister of marbles onto the floor. But Robin wasn't moving at all when this happened. Trying to walk over marbles will make you fall. Standing still while marbles roll around and bounce off your feet? Not so much.
Continuity mistake: In this episode, Chris thinks back to when he went back to the past. When he and Bianca are on the tour of the manor, there are some costumes that have been worn by the charmed ones. But in the episode "Oh My Goddess (1)" Chris tells Phoebe that Paige died on that day, so how could she have worn something after she died? And if she did die that day, Chris would have never met her, since he was not yet born, and could not have learned to orb from her, as he says in "Spin City." However there are other inconsistencies with that story that Chris mentions later, seeming to suggest he lied about this to get the sisters onside. It may not be a continuity error but as it was never fully addressed in the show just what Chris was lying about (and he obviously told some) we cannot be sure.
Other mistake: When Phoebe arrives back from her vision quest to find Piper has been kidnapped she tries to sense from the frozen students which one created the headless horseman. As Gideon, Paige, Chris and Phoebe walk into the conservatory you see Zachery blink rather obviously.