I’ve decided to do a list of South Park’s continuity’s errors:
In the episode "Cartman's Mom Is Still a Dirty Slut”, Kenny comes back to life by magically reappearing and the characters (at least Kyle) are shown to be aware of this. In the episodes "Cartman Joins NAMBLA" and "Coon Vs. Coon And Friends" Kenny comes back to life by being reborn through his mother and the characters are unaware of him dying.
A few episodes mention that Kyle's family moved to South Park when he was about three. In "It's A Jersey Thing," however, it's a plot point that they moved there while Sheila was pregnant with him.
There have been several examples of minor characters' names changing, and even more important secondary characters have inconsistent surnames (Token Williams becomes Token Black, Jimmy Swanson becomes Jimmy Valmer, etc.)
In "My Future Self 'n Me", one lyric in the song implies that Stan is clean while his "future self" actually just a guy posing as Stan's future self isn't. In "Pee", we find out that Stan doesn't wash his hands.
In "Proper Condom Use" (Season 5), Butters says that he's turning 9 next week. In "Cartman Sucks" (Season 11), he says he's still 8.
In "Breast Cancer show ever", Wendy says that no one does nothing when Cartman is doing something immoral, but in several episodes, particularly in "Cartoon Wars parts 1 & 2" and "La petit Tourette", Kyle tries to stop Cartman of doing something immoral.
This episode also implies that Cartman has never been beaten by a girl before, but in "Cat Orgy", he was shown to be beaten by Shelly more than twice.
the episode "Trapped Keeper" shows that Ike started to go to school, but in "Cancelled", Ike is still shown to not go to school, as he follows Kyle to bus stop, however, later episodes, most notably in "Miss Teacher Bangs a boy" and "Royal Pudding", Ike is shown to go to school.(although this must be a continuity error that was already fixed in recent seasons).
Randy (a geologist) is mentioned as the only scientist in town, but later Token's mother is said to be a chemist, and Clyde's father a geologist. And later Clyde's father is not a geologist but a shoe store owner.
Kenny is revealed to have a younger sister in "Best Friends Forever", when previously the McCormicks were stated to have two children. Matt Stone admitted that she was an oversight, and she didn't reappear for a while until "The Poor Kid". It has since been revealed that Kenny did have a younger sister in early plans for the series. She was meant to be around Ike's age, and was mentioned in an early script for "Starvin' Marvin" (though she did not make it into the final product).
The episode "Butter's Bottom Bitch" (S13 E9) begins with Cartman and some of the other 4th grade boys making fun of Butters because he had never kissed a girl. In all actuality, Butters was kissed by Rebecca Cotswold in "Hooked on Monkey Phonics" (S3 E13).
Cartman and Shelly became friends by the end of "Cat Orgy", but in "The New Terrance and Phillip movie trailer", Cartman and Shelly still hate each other.
The movie has a few continuity errors that contradict the show itself:
Perhaps the most obvious example is that the movie claims that the boys used to not swear before watching The Terrance and Phillip movie, but prior to the movie, they were shown to swear a lot.
By the end of "Ike’s wee wee", Kyle started to regard Ike as his brother despite the latter being adopted, but in the movie, Kyle still doesn’t accept him as a true brother, however, this continuity error must be exclusive to the movie as in the actual show, especially in later seasons, Kyle is shown to truly accept Ike as his brother, particularly in "It’s Christmas in Canada" and in "Taming Strange".
Sheila is portrayed as a sociopathic extremist in the movie, while is true that she always was a overbearing moral guardian in the show, she never went as far to want to destroy a entire country because of it TV show.
However, is heavily implied that the movie is not canon.