The Demon Who Came In from the Cold - S3-E19
Visible crew/equipment: After Prue removes the piece of Belthazor flesh from the freezer it cuts to Cole finding Phoebe's note in his pocket with a closeup of Cole, and at the start of the next shot the reflection of the boom operator holding up the boom pole and mic can be seen on the glass window, behind Pirelli/Vornac. (00:28:05)
Continuity mistake: After Prue and Phoebe send contagious Piper back up to bed, it cuts to three consecutive shots of buses arriving at camp. In the first shot, the bus license plate is white with the number "2IAB345" and we see markings on the bus as the counselor exits. The second closer shot shows two kids exiting the bus. Then in the third wideshot, with those same two kids beside the door, the license plate is now blue with the number "876QPD" and we see the same markings on the bus as in the first shot, so we know it's the same bus. (00:22:05)
Visible crew/equipment: After Lukas kills the other demon so he can move forward with his plan to go after the witches, when it cuts to the manor's foyer as Prue and Phoebe walk in, the green T-mark is visible on the rug at the bottom of the screen. (00:08:15)
Visible crew/equipment: After the Grimlocks enter the manor Leo calls for Piper then rushes out of the kitchen, and when it cuts to the shot of the dining room the edge of the crew's black mat is visible at the bottom of the screen. The black mat is again when the sisters are pulled into the time portal, though the only thing we should be seeing is the fringed area rug. (00:04:00)
Continuity mistake: While Dantalian tries to steal the Book of Shadows from the attic Piper and Phoebe surprise her, then when Phoebe kicks Dantalian and she falls we see the stuntwoman's footwear has chunky sole ridges, but when the sisters approach Dantalian her shoes have heels. (00:32:10)
Blinded by the Whitelighter - S3-E11
Visible crew/equipment: After the opening credits, when it cuts to Piper and Leo in the dining room the green tape mark is visible under the table, and the red T-mark and long blue tape mark are also visible on the crew's black floor mat behind Leo. (00:04:45)
We All Scream for Ice Cream - S3-E10
Visible crew/equipment: When Phoebe gets an IM on the laptop Prue walks over to her, and just as Prue sits down at the table we can see the blue tape mark on the floor, where she had been standing. (00:05:50)
Visible crew/equipment: After following the signs that lead to the demolition site, when Prue unlocks the chain on the door and enters the loft, the T-mark is visible on the floor at her feet. (00:03:45)
Visible crew/equipment: After Phoebe tells the others that Emilio will be getting arraigned at night court in an hour, when it cuts to Leo and the sisters walking in the court hall, the shadow of the boom mic is moving at the top, left side of the screen. (00:33:45)
Be Careful What You Witch For - S2-E22
Revealing mistake: During the search for the Dragon and teenage Prue, Phoebe's wearing a red top and red jacket, but when Phoebe lands on the ground we can see the bulky beige material of the stunt vest at her back, under the red top and jacket. (00:34:05)
Be Careful What You Witch For - S2-E22
Visible crew/equipment: While Leo is up in the attic with Piper, flying Phoebe, and teenage Prue, Leo explains what happened to Prue, and when Phoebe asks how it's even possible, we can see the stunt harness at the back of Phoebe's jeans as she rises in the air. (00:18:45)
Visible crew/equipment: When the sisters hide the chimps in the laundry cart to slip out of the hospital, the blue T-mark is visible on the floor at the bottom of the screen, before they peek around the corner and notice the TV. (00:20:15)
Continuity mistake: When Prue shows her sisters the article in 415 Magazine with her photo credit, in the closeup we see that Prue opens the magazine with the article and Maggie's photograph on the page to the right, but in the next shot facing Piper and Phoebe the magazine is folded open and they're looking at the page to the left with an entirely different page to the right. (00:40:40)
Visible crew/equipment: After Phoebe has turned everyone in P3 into animals, when Phoebe stands at the bar the white T-mark is visible on the floor at her feet, twice. (00:35:00)
Continuity mistake: When the ani-men break into the manor the entire large center glass of the left door ends up broken, but later while Phoebe is looking for the hydrogen peroxide, Prue notices the front doors and the left door's center glass is intact with only the bottom corner broken. (00:22:00 - 00:27:05)
Continuity mistake: After the manor is broken into, in the following shots while everyone is in the foyer the left front door is wide open in most shots, but in some other shots both front doors are closed during this scene. (00:21:50)
Continuity mistake: After class, when Phoebe is talking to her study group she pulls out the flyer for P3, and in the first shot the flyer is in Phoebe's right hand, but in the next shot she's holding it out in her left hand. (00:01:40)
Visible crew/equipment: While Phoebe is telling Prue about the abandoned baby, Piper comments that the baby is like a car alarm, and as the sisters walk into the foyer the white T-mark is visible on the rug in the foyer. (00:07:20)
Visible crew/equipment: After the shots of the kids arriving on the first day of camp, when it cuts to Prue and Phoebe in the car, we can see the reflections of the camera operator and camera dolly on the surface of the car. (00:22:35)
Continuity mistake: After Phoebe tells Piper about the balloon plan, when Piper starts talking about Leo she fills the blender on the counter, and in the two shots facing Piper the white lid is on top of the blender, but in the shot facing Phoebe the lid is gone before she turns it on. (00:19:10)
Answer: That was a mistake in the series.
Also, the episode is called 'Babies First Demon' and this alone tells us that it's Wyatt's first time in the field (so to speak) and as the sisters say, they've done a good job of clearing up their own magical messes so far. Nobody really knows how advanced Wyatt's powers are, or will become. That's why the cleaners appear, to nip things in the bud. The Cleaners didn't want to chance that the sisters could clean Wyatt's magic up, just incase they couldn't. Therefore intervening themselves, just in case.