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 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 Zarnecki Incursion - S4-E19
Plot hole: If Howard can hack into Blizzard's database so deeply that he can get the name and address of game players, he could easily restore all of Sheldon's stolen 'items'. Hacking personal details - a player's real identity and their home address! - is hardcore, detailed work that only an expert could do, compared to which adding a few extra items to a player in the game would be child's play. Sheldon would not be concerned about a possible comeback from the administrators at Blizzard. First, Sheldon doesn't hack into the database, Howard does, and someone as pragmatic and self-centred as Sheldon would simply disclaim any responsibility. Second, hacking into another player's account to access highly sensitive personal information like their home address would risk incurring the same penalty from Blizzard anyway. Either Sheldon doesn't know that or he doesn't care. Third, his account has already been hacked when the virtual items were stolen. He could simply claim that Howard's hacking into his account was just more of the same - nothing to do with him. Fourth, Blizzard did not detect the hacker stealing Sheldon's virtual items, nor did they prevent it happening, and they did not detect Howard hacking into his account to obtain his name and address. Sheldon can rightly assume he has nothing to fear.
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 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 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 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 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 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 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.
Suggested correction: Hacking the database to return items to Sheldon's account would also be traceable to Sheldon's account as cheating. That would get him permabanned if discovered, not a risk Sheldon wants to take.
LorgSkyegon
First, Sheldon doesn't hack into the database, Howard does, and someone as pragmatic and self-centred as Sheldon would simply disclaim any responsibility. Second, hacking into another player's account to access highly sensitive personal information like their home address would risk incurring the same penalty from Blizzard anyway. Either Sheldon doesn't know that or he doesn't care. Besides, if Blizzard were aware that Howard had hacked into Sheldon's account, why weren't they aware that the person who stole the virtual items did?
Reading information from a server is easier than writing new data into it. You can steal a mass bulk of files and extract the information at a later time, whereas writing information in Sheldon's account would take much more precision.