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 Herb Garden Germination - S4-E20
Revealing mistake: When Sheldon is web chatting with Amy, we can hear Amy talking, but the bar at the top of Sheldon's computer screen indicates that the sound is off.
The Cohabitation Formulation - S4-E16
Character mistake: When Penny says she smells Chinese food and Sheldon corrects her by telling her she's slipping because it's Thai, Sheldon is eating the food with chopsticks, even though in a previous episode he uses a fork and spoon because that's how Thai people eat their food. (00:19:15)
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.
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 Agreement Dissection - S4-E21
Continuity mistake: When the girls take Sheldon out dancing, he mentions that he considers himself a proficient dancer due to his Cotillion training when he was a boy. But in S1E7 The Dumpling Paradox, when Leonard suggests that they could have gone dancing with the girls, Sheldon said that nobody in the group - including him - could dance.

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 Herb Garden Germination - S4-E20
Other mistake: When Sheldon and Leonard are playing Archery on Wii Sports Resort, Sheldon presses the Z button on the nunchuck controller to fire the arrow, which is incorrect. When Leonard plays, he holds the Z button as he prepares to fire, then releases the Z button to fire, which is the correct controls. (00:03:00)

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 Zarnecki Incursion - S4-E19
Plot hole: While it would certainly destroy the entire plot of the episode, Sheldon could have simply contacted Blizzard's customer support to get all his stuff back.
The Wildebeest Implementation - S4-E22
Continuity mistake: When Howard, Bernadette, Leonard and Priya are playing Jenga on the coffee table, the silver coffee pot, between the game and a coffee cup, disappears and reappears between shots.
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 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 Cohabitation Formulation - S4-E16
Continuity mistake: When Penny is pouring water into the glasses on the table after first meeting Raj's sister. The level of water in the pitcher changes between shots
The Herb Garden Germination - S4-E20
Revealing mistake: Sheldon's laptop has gone through several strange transformations throughout the series, but in this episode it takes the biscuit - it appears to be a Dell XPS with the back covered up, but the shot of Sheldon chatting only to Amy shows a Mac keyboard, with the laptop running OS X.
The Benefactor Factor - S4-E15
Continuity mistake: When Sheldon and Leonard are in the kitchen discussing Leonard's upcoming night out with Mrs. Latham, there's a plastic bottle of orange juice on the table that keeps disappearing and reappearing as the camera switches between Sheldon and Leonard.
Suggested correction: The bottle is there every time, a few times because of the camera angle it is hidden by Sheldon.
The bottle of OJ is right next to a container of Coffee Mate, both items always visible when the bottle of OJ is present. When the OJ is not present, only the Coffee Mate is there, near enough the center of the table to not possibly be blocked out by either Sheldon nor Leonard.
No it is not right next to the coffee Mate, there is some distance with a phone in between. You can sometimes see the bottle behind Sheldon when he moves.
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
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 Robotic Manipulation - S4-E1
Continuity mistake: When Penny says "let's just finish our dinners" she raises her fork twice. (00:16:45)
The Zarnecki Incursion - S4-E19
Character mistake: As they drive to Todd Zarnecki's to confront him, Sheldon says, "I almost feel sorry for the poor fool, sitting in his split-level suburban ranch..." Architecturally, split-level (technically three levels joined by half flights of stairs) and ranch (single level) are separate and distinct designs. There is no "fusion" of the two. I can't help but think Sheldon would have corrected anyone who said the same thing.
Suggested correction: Actually the term "split level ranch" is used to describe a house that has one full floor above ground and a partial lower level, vs the traditional split level house which has a full floor above ground, a second partial floor and a partial lower level.