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.
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 Prestidigitation Approximation - S4-E18
Continuity mistake: Near the end of the episode, in the canteen scene, Howard shows the card trick to Sheldon again. The card at the bottom of the deck is the 2 of hearts as he takes them from the box. Sheldon then takes this card from near the top of the deck when Howard puts them on the table. The deck is not shuffled between times.
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 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 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 Prestidigitation Approximation - S4-E18
Continuity mistake: It is well-known that Leonard's glasses do not have lenses to avoid catching reflection by the lights. In this episode, Priya takes Leonard's glasses off, and they have lenses.
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 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 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)