The Spaghetti Catalyst - S3-E20
Continuity mistake: When Raj and Leonard are sitting on the couch, Leonard is holding Watchmen and Lost in Space in his left hand and Young Sherlock Holmes in his right. In the very next shot when Leonard turns his head after Raj speaks, Watchmen has disappeared.
The Plimpton Stimulation - S3-E21
Continuity mistake: When Sheldon, Penny, and Leonard are discussing Leonard's tryst with Dr. Plimpton, Penny pinches the bridge of her nose with her right hand. The shot changes and Penny brings her left hand down from her face.
The Staircase Implementation - S3-E22
Character mistake: In 1-14 "The Nerdvana Annihilation", when Howard says they should put the time machine into the elevator, Leonard states the elevator had been broken for two years. But in this episode, we found out the elevator broke seven years earlier. (00:03:10)
The Robotic Manipulation - S4-E1
Continuity mistake: At the start, as Howard says "And finally my kung pow chicken" the robot arm is level with the top of the bag. Camera cuts and it's reaching to the bottom of the bag. (00:00:15)
The Robotic Manipulation - S4-E1
Continuity mistake: When driving to the date, the cars behind Penny's change place instantly. For example a 4x4 becomes 3 cars, which become 1 car in the space of 3 seconds. (00:09:10)
The Robotic Manipulation - S4-E1
Continuity mistake: When Penny says "let's just finish our dinners" she raises her fork twice. (00:16:45)
The Robotic Manipulation - S4-E1
Continuity mistake: The lemon wedge in Amy's water flips back and forth throughout the dinner scene. (00:17:00)
The Robotic Manipulation - S4-E1
Continuity mistake: In the ER, the glasses around the nurse's neck move instantly without her touching them. They go from angled to straight instantly. (00:17:45)
The Cruciferous Vegetable Amplification - S4-E2
Character mistake: In the first scene, on Sheldon's board are the words "D-D Fushion." This should be fusion. Sheldon wouldn't make a mistake like that.
The Hot Troll Deviation - S4-E4
Continuity mistake: When George Takei and Katee leave Howard's bedroom, in one shot Howard is clasping his hands together, in an instant they are spread out completely. With no time to move them. (00:04:25)
The Hot Troll Deviation - S4-E4
Continuity mistake: When Leonard and Howard are talking at the University, Leonard says "Oh my god you ran over a hobo!" when he does so Howard is not holding his fork, camera cuts and he suddenly has his fork in his hand. (00:05:15)
The Hot Troll Deviation - S4-E4
Continuity mistake: When Sheldon and Raj are arguing about having a desk in Sheldon's office, Sheldon's bottle of water keeps rotating without anyone touching it - take note of the label. The level of water in Sheldon's drink also keeps changing between shots. (00:06:20)
The Hot Troll Deviation - S4-E4
Continuity mistake: When Howard and Bernadette are talking in the Cheesecake Factory, her apron that she puts on the table is constantly changing position. (00:12:30)
The Hot Troll Deviation - S4-E4
Factual error: During the final scene of this episode, Sheldon steps out of his office wearing a gas mask and engages Leonard in conversation where he then states he is making hydrogen sulphide gas (more commonly known as H2S). Leonard correctly identifies this as highly flammable. However, this gas is far more dangerous and is harmful to the human body at as low a concentration as 20 parts per million (ppm), can cause permanent damage at 100ppm and is fatal after two breaths at 500ppm. So for Raj (and his bird) to be completely unharmed in a high concentration of H2S (noted by the fire) is impossible.
The Hot Troll Deviation - S4-E4
Factual error: Howard's claim that characters in World of Warcraft can engage in sexual activities is wrong, also while there is a Bridge of Souls currently in the game, there is no way to get under it.
Suggested correction: I can only assume you have never played on a RP server? ERP is a big thing, some players even make gold from it.
The Irish Pub Formulation - S4-E6
Continuity mistake: As Raj, Howard and Sheldon are sitting at the table discussing leaving Priya alone while Leonard and Priya are away from the table, a water bottle sitting in front of Raj moves back and forth between his tray and Leonard's tray.
The Apology Insufficiency - S4-E7
Continuity mistake: When Sheldon is drink his shots, the amount in his shot glass increases before he takes final shots.
The Boyfriend Complexity - S4-E9
Continuity mistake: In 2-15 "The Maternal Capacitance" Penny explains to Beverly, referring to her father, "My mom could have just said 'Bob, get over it, she's a girl'". But in this episode Penny's father is named Wyatt.
The Justice League Recombination - S4-E11
Character mistake: Even with Penny and Zack the guys are one man short to be the original JLA because they they don't have the Martian Manhunter. If they used the same costumes in the previous year, they would have been three people short of the original line-up.
The Thespian Catalyst - S4-E14
Revealing mistake: When Sheldon goes to Penny's apartment and they do a scene study together, they both read lines from a multi-page script that Sheldon brings with him. On a couple of occasions the camera cuts to a side view of Sheldon and we get to see the page of the script that he's currently reading from. The pages are completely blank.