Bottom's Up - S1-E5
Continuity mistake: When Richie and Eddie are on the roof and Richie starts his rain dance, watch the bottom of his trousers. To start of with he pulls the hem up to around his shins. He then starts and pulls his groin or something and stops and at this point the right hand trouser falls back down his leg. Then straight afterwards in the long shot you can see that it's back up again without him pulling it up.
Revealing mistake: When Eddie ties the string to Richie's leg and slams the door, watch the leg. The jeans actually rip and the fake leg comes out and you can even see the actor's real leg tied underneath. It's really obvious in slow motion.
Apocalypse - S1-E4
Revealing mistake: After the piano falls from the ceiling, Ritchie rumbles Eddie's "plan" and kicks him out of the flat. When Eddie is pushed out the front door and down the stairs you can see him falling to begin with, but halfway through he actually stops as if he's kneeling, then ducks out of shot. The sound effects lead us to believe that he's fallen all the way down the stairs and been attacked by a pack of dogs at the bottom.
Continuity mistake: When Richie is telling the other 3 guys to go to the corner, he still has his hands on the wheels of his chair. But when the shot changes and Richie says "if you need the toilet then put your hand up", his arms are crossed around his waist.
Revealing mistake: When Ade Edmondson clamps the pliers onto Rik Mayall's nose, if you watch carefully you can see the pliers bend a couple of times, showing that they are made of rubber or something similar. (00:13:45)
Continuity mistake: When Richie falls off the ladder, it's apparent from the way he falls that he lands on his front (you just see his leg pop into shot) and that his head would be pointing towards the camera. However, instantly in the next shot we see him on his back with his head towards the wall.
Apocalypse - S1-E4
Revealing mistake: When Eddie falls through the ceiling playing the piano, it's very obvious from the back that it's a dummy because it wobbles around but is stuck to the seat.
Bottom's Up - S1-E5
Continuity mistake: When they are first on the roof, Richie is seen looking through a telescope on a stand. However, it is gone a few moments later, and doesn't appear at all for the rest of the episode.