The Truth Is Out There... and It Hurts - S1-E8
Revealing mistake: When Phoebe asks Piper what she thinks of her boss, you can see that Holly's tattoo has been covered up, because that part of her wrist is darker than her skin. (00:17:15)
Suggested correction: Maybe Holly covered it up with makeup because she isn't supposed to have tattoos for her job? A lot of jobs still don't allow piercings and tattoos today but all those years ago it was even harsher.
There are multiple instances of covered tattoos during the early seasons. I noticed it the most on Alyssa's back tattoo.
Love Hurts - S1-E21
Revealing mistake: After Piper saves Leo, they meet with Phoebe and Daisy downstairs near the living room. Before the darklighter appears, smoke from a fog machine can be seen at the left of the shot to magically transition to the computerized effects. (00:33:45)
Revealing mistake: When Mark (as a ghost) and Piper leave the hotel after he asks for her and Phoebe's help, he bumps into the handrail as he walks down the steps.
I've Got You Under My Skin - S1-E2
Revealing mistake: At the end of the episode when Phoebe and the other two are at the bar you can notice that Prue straw in her drink goes in and out of her drink a great deal.
Revealing mistake: Prue is needed in the storm drain to rescue Piper, who is stuck in a hole bottomed off by a metal circular guard. Prue uses her power to levitate the metal circle to her level. When the camera pans out, the metal rods used to actually levitate the metal circle are visible. (00:36:25)
Which Prue Is It, Anyway? - S1-E16
Revealing mistake: When Pink Prue is stabbed, they show the warlord over her, with the sword supposedly having stabbed her body. It is very obvious that the sword is not actually in her, but about a foot away from her body, closer to the warlord.
Revealing mistake: In the scene where Penny uses her powers at Nicholas and throws him on the dining table, it is clear that the table is a fake one simply made of simple wooden boards.