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: 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: 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: 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?
Plot hole: When Piper and Phoebe appear in the past, Penny chides them not to "use [their] magic so openly." Immediately thereafter, Penny uses magic to turn some police officer's night sticks into flowers. That was some pretty open use of magic, right there.
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: 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.
Plot hole: Why doesn't Chris ever use his powers against demons? We know he can use them in this time, since he blows up Leo in "Oh My Goddess" and kills a Valkyrie in "Valhalley of the Dolls", and after "Chris-Crossed", when it was discovered he was half-witch he had no reason to hide them from the sisters, yet he never once used them against a demon, even when one of the Charmed ones is in mortal danger.
Plot hole: When Paige tries to orb to prove her identity to Chris, she can't because Margo has cast an anti-orbing spell. But that's not possible. The Charmed Ones and Chris all orbed into the room, and Margo couldn't have cast a spell after that, or we would have seen it happen.
Plot hole: After Paige changes the past, the ghost of Grams changes from a no-nonsense demon-hunter into a pacifist hippie. So, apparently, we are now in an alternate timeline where Grams never became assertive, and stayed a hippie all her life. The episode went to great lengths to establish that if Grams had stayed a hippie, she and the Charmed Ones would have all died young. But the ghost of Grams was still middle-aged, instead of decades younger, and Wyatt and Chris were still there, but they wouldn't have been if their mother Piper had died as a child.