Other mistake: After Sam uses the powder on the sisters, erasing their memories, they're visited by Leo who starts to say "he must have gotten the powder" and one of the sisters finishes with "our mother." But in a later episode we learn all white lighters have this powder.
Revealing mistake: When the pawn shop owner jumps through the glass door, it is painfully obvious that it's a stunt double.
Revealing mistake: When Phoebe opens the cupboard and the human pig falls on top of her, you can see that it's a stunt double in the far shot.
Visible crew/equipment: Just after Piper freezes the security guard after she and Prue enter the prison, they are walking along a corridor and the shadow of a boom mic can be seen in the top left quadrant of the screen.
Continuity mistake: When Phoebe is attacked by Anton's spirit, she puts her right hand over her throat twice. (00:03:15)
Continuity mistake: When Piper confronts Phoebe about casting the spell to help her decide between Dan and Leo, Phoebe's finger jumps to the back of her ear, then disappears. In a following shot, her finger is now resting on her neck. (00:09:45)
Plot hole: It is stated Leo is born on May 6th, 1924. Yet he was in his 20's as Piper's ex-lover in his past life around 1924. It also stated that that is when he died and became a whitelighter but the war wasn't until 1942. He died shortly after that meaning he didn't become a whitelighter until after 1942.
Other mistake: When Prue astrals back to recite the spell to reverse the awakening spell, she and Phoebe don't actually complete the spell, they just recite the first paragraph "What was awakened for its sleep, must once again slumber deep" the rest according to the book of shadows is "return the disease to whence it came, so life can ease back to the same".
Continuity mistake: When Matthew starts crying and Piper freezes him, Prue puts her hands on her forehead. In the following close up, her hands are brushing her hair back, then back on her forehead in the next wide shot. (00:23:00)
Continuity mistake: The first three episodes have zero continuity when it comes to Piper's love life. In Ep1 "Witch Trial" Piper is hooking up with the guy who is looking at the loan for P3. Then in Ep2 "Morality Bites" she is with Leo (presumably they have secretly been together for months as they discuss their many issues being able to talk when they're both so busy with magic crises and how Leo hasn't figured out how they can be together without clipping his wings). But by Ep3 "The Painted World" Piper and Dan are already together. They has been no discussion of Piper and Leo breaking up and zero mention of Piper and Dan getting together (in fact, the last time we saw Dan in Ep1, he and Phoebe were flirting pretty heavily). I am so confused and I do not at all remember these inconsistencies from when I first watched these episodes years ago. Were these shot and aired out of sequence or something?
Suggested correction: Your last statement is correct, which also invalidates your error. Ep3, "The Painted World" was produced before Ep2, "Morality Bites" but "Morality Bites" was aired first, out of sequence.
Suggested correction: Piper and Dan weren't together in The Painted World, they weren't together until she's a man, baby, a man. When Piper sees his dating tape.