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.
Visible crew/equipment: When Aviva tells Phoebe that she wants to go upstairs because she's not feeling well, Aviva walks into the bedroom and just as she grabs her backpack part of the T-mark is visible on the floor where she stands. (00:33:45)
The Truth Is Out There... and It Hurts - S1-E8
Continuity mistake: In the teaser, the demon attacks Dr. Mitchell, killing him and also destroying his irises. His eyes turn white, and later dialogue confirms that the irises were gone from his eyes. However, when the Charmed Ones find his corpse, his eyes are open and his irises are visible. (00:01:10)
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.
The Truth Is Out There... and It Hurts - S1-E8
Continuity mistake: In this episode the truth spell is before the demons page in the Book of Shadows, but in 'Out of Sight' the truth spell is after the demons page.
Continuity mistake: When Prue describes the way the warlock Matthew traveled instantaneously, Melinda tells the sisters that it's called blinking, and that Matthew "must have copied it from another witch." But later in the series, every warlock encountered by the Charmed Ones had the ability to blink, and it was considered exclusively a warlock ability, meaning that no witch would have had it. (00:21:30)
Character mistake: In the attic, Melinda Warren is awed at how thick the Book of Shadows has gotten. But according to information from previous episodes, the Book was started after Melinda had died, so she wouldn't know how thick or not it was.
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.
Factual error: In the opening scene in Salem, Melinda Warren is going to be burned at the stake. But in the real Salem trials, no one was burned; all of the people convicted of witchcraft were hanged.
Continuity mistake: When Prue lets Matthew out of the locket, the front view Prue has her right hand on her stomach, when the shot changes to the back view her hands are by her side, it does this multiple times.
Factual error: Melinda Warren says that after Matthew turned her in to the council, she was burned at the stake for being a witch, except witches were not burned at the stake, they were hanged.
Wicca Envy - S1-E10
Continuity mistake: At the beginning of the episode when Piper hides her sisters from Leo she has the shirt with the buttons closed, but between that scene the shirt is not closed. (00:01:05)
Wicca Envy - S1-E10
Visible crew/equipment: After Jaime tells Prue that she's the hardest working woman he's ever met and believes she's innocent, Prue walks into the office to access Hannah's computer, and just as Prue sits down and moves closer to the desk, the blue T-mark is visible on the floor, under the office chair. (00:24:30)
Wicca Envy - S1-E10
Continuity mistake: At the end of the episode, when Leo and Piper are saying goodbye he reaches out and touches her face, but when the angle changes his hands are instantly back at his side. (00:43:05)
Wicca Envy - S1-E10
Audio problem: When talking about the tiara with a security guard Prue's mouth stops moving mid sentence but the audio continues.
The Wendigo - S1-E12
Visible crew/equipment: When Phoebe joins her sisters in the kitchen before her first day at work, the reflection of the moving boom mic is visible on the glass cabinet, at the top of the screen. (00:10:05)
The Wendigo - S1-E12
Continuity mistake: When Andy is lying on the ground unconscious The Wendigo rips open his shirt popping all the buttons, but in the closeup of Andy's face his shirt is still buttoned up. (00:38:50)
From Fear to Eternity - S1-E13
Visible crew/equipment: When Andy walks into the manor to speak with Prue, just as she tells him it must be bad news, we see the reflection of the boom mic on the glass door. (00:09:45)
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?