Throughout some episodes of The Big Bang Theory, there have been some contradictions, which include the following:
Sheldon is sarcastic to Leonard, telling him that "Archimedes would be so proud" in the "The Big Bran Hypothesis" (Season 1 Episode 2) when Leonard fails after invoking the mathematician's name and teachings. In the following episode, "The Fuzzy Boots Corollary," however, it is made apparent several times that Sheldon does not understand sarcasm and even needs a SARCASM sign. It may possibly be that Sheldon knows what sarcasm is, but he can't tell when other people are using it.
Sheldon with the cats.
In "The Fuzzy Boots Corollary", Leonard mentions Sheldon gets asthma when he is around cats. In "The Griffin Equivalency" (Season 2 Episode 4), Sheldon said that his family had a pet cat named Lucky. In "The Zazzy Substitution" (Season 4 Episode 3), Sheldon buys 25 cats when Amy "broke up" with him. He could take medication for it, which is what many people do.
In "The Maternal Congruence" (Season 3 Episode 11), Sheldon cheers for the Grinch's meanness and finds it a buzzkill when he succumbs to social convention and gives the presents back. In a different episode, Sheldon compares Stuart to the Grinch in a bad way, demonstrating he knows of the negative connotations of the Grinch.
Early in season 1 - "The Luminous Fish Effect" (Episode 4) - Sheldon tells Penny that he is 140 pounds when he goes to the market with her. However, near the end of season 1 - "The Porkchop Indeterminacy" (Episode 15) - he tells his sister, Missy, to tell their mother that he is 165 pounds, which would be a 25 pound increase in only a few months. It's possible this was just lip service to keep his mother off his back.
In "The Luminous Fish Effect" (Season 1 Episode 4), Sheldon estimates that the car he and Penny are riding in is about 4000 pounds. This cannot be correct, as it is a Volkswagen Rabbit (Golf Mk 1) and would be approximately 2000 pounds, maximum.
In the "The 21-Second Excitation" (Season 4 Episode 8), Sheldon recalls how he made Leonard wait in line for Star Trek: Nemesis to get good seats, though that film was released in 2002 and Leonard and Sheldon didn't meet until 2003, according to the flashback episode, "The Staircase Implementation" (Season 3 Episode 22). Given the tepid response to the film by the public at large, it's unlikely there was a revival showing of it, unless it too had unseen footage that would have made the movie better.
In "The Luminous Fish Effect" (Season 1 Episode 4), Sheldon gave a complicated explanation of what he did with his life past fifth grade, which combined would make him 23 at that time. However, in "The Friendship Contraction" (Season 5 Episode 15), Leonard stated that Sheldon was 30. Given the information in "The Luminous Fish Effect", Sheldon would only be 27 in "The Friendship Contraction."
Amy's name tent does not have "Dr" on it, unlike Raj's, despite both having PhDs.
In "The Love Car Displacement" (Season 4 Episode 13), Amy's name tent did not have the title "Dr" in front of her name, while Sheldon's, Leonard's, and Raj's did. Obviously Howard's didn't. This is a contradiction manifested as a prop error because the show later reveals Amy does, in fact, have a doctorate.
In "The Good Guy Fluctuation" (Season 5 Episode 7), Stuart congratulates Leonard for being the first person to pick up a girl in Stuart's comic book store. However, Stuart himself picked up a girl (Penny) in the comic book store in season 2 (Episode 20: "The Hofstadter Isotope").
In "The Pancake Batter Anomaly " (Season 1 Episode 11), Sheldon tells Penny that he once got sick alone in Germany when he was 15 years old and because his mother had to fly back to Texas to help his dad. This clearly suggests Sheldon's dad was alive when he was 15. However, in "The Thanksgiving Decoupling " (Season 7 Episode 9), Sheldon tells Mr. Rostenkowski that his father died when he was 14.
In "The Gothowitz Deviation" (Season 3 Episode 3), Sheldon told Penny he doesn't dance, even in an infinite number of universes. However, in "The Agreement Dissection" (Season 4 Episode 21), Sheldon said he's an excellent dancer. Sheldon proves that later in the episode when skillfully dancing with Amy. It is also well established before this in "The Fuzzy Boots Corollary" (Season 1 Episode 3) and "The Middle Earth Paradigm" (Season 1 Episode 6) that the boys do not like dancing. However, this could be Sheldon warming up to the girls, especially Amy.
Sheldon makes a categorical error in "The Bat Jar Conjecture" (Season 1 Episode 13). When Howard says he should answer the engineering questions because he is an engineer, Sheldon compares this to him answering all of the anthropology questions because he is a mammal. Anthropology is the study of humans, not mammals; all humans are mammals, but not all mammals are humans. He ought to have said mammalogy, or claimed he was a human.
In "The Killer Robot Instability" (Season 2 Episode 12), Sheldon and the guys want to improve their fighting robot, but Sheldon doesn't even know how to open the tool box, which implies he has no mechanical skills. Sheldon claims that while he grew up in Texas he built a CAT scanner out of his sister's EasyBake Oven, a sonic death ray, and tried to build a nuclear reactor, thus having some skills to invent things.
In "The Roommate Transmogrification" (Season 4 Episode 24), Bernadette turns down the heart disease project because neither of them have heart problems. In the previous episode, "The Engagement Reaction", Howard claims that his family is the history of heart disease after his mother his sent to the hospital.
This is more of a fallacy and not so much of a contradiction, but in "The Euclid Alternative" (Season 2 Episode 5), when Sheldon asks Howard to change the color of the car in the simulator he says, "You know the pale blue of Luke Skywalker’s lightsaber, before it was digitally remastered?" Luke Skywalker's lightsaber is green, as is demonstrated in Episode VI: Return of the Jedi, because he built it. The pale blue lightsaber he uses in Episodes IV and V is his father's, Anakin Skywalker's.
The famous flashback episode, "The Staircase Implementation" (Season 3 Episode 22), details Leonard moving into Sheldon's apartment seven years prior to the episode, putting the events of the flashback in May 2003. However, in "The Stag Convergence" (Season 5 Episode 22), when Sheldon is comforting Howard, he says, "Also, there was a single cube of chicken bouillon in the cupboard when I moved in and it’s been bothering me for the last eight years. So, as they say, two birds." The events of "The Stag Convergence" took place in May 2012, making Sheldon's reference of him moving into the apartment eight years ago at 2004, a year after Leonard is supposed to have moved in. Theoretically, one could claim the cube of chicken bouillon did not bother Sheldon for a full year after he moved in but that seems unlikely for our lovable Sheldon Cooper.
In "The Codpiece Topology" (Season 2 Episode 2), Leonard struggles to find examples of his previous girlfriends beyond Joyce Kim and Leslie Winkle. However, in the previous episode, "The Bad Fish Paradigm," Sheldon tells Penny that Leonard used to date a woman with a PhD in French literature. Unless Joyce Kim has a PhD in French literature, Leonard totally forgot a girlfriend.
In "The Adhesive Duck Deficiency" (Season 3 Episode 8), when Sheldon is driving Penny to the hospital, he becomes distressed that Penny's car's check engine light is on. This is a double contradiction/inconsistency. Previously, in "The Financial Permeability" (Season 2 Episode 14), when Penny is explaining how she got behind on her bills due to her car breaking down, she said, "Well the check engine light is fine. It’s still blinking away. It’s the stupid engine that stopped working. It cost me like twelve hundred dollars to fix it." The period between "The Financial Permeability" and "The Adhesive Duck Deficiency" is nine months. Unless Penny did some serious harm to her car in that time period, her engine should have been fine from fixing it in "The Financial Permeability." However, even before "The Financial Permeability," it is first established Sheldon learns of her check engine light in "The Euclid Alternative" (Season 2 Episode 5). So Sheldon should have already been used to Penny disregarding practical vehicular maintenance.
In the beginning of "The Romance Resonance" (Season 7 Episode 6), Sheldon is "in the zone" at The Cheesecake Factory. When Penny asks what he's doing, Amy responds with, "Could be anything. Last time he was like this, he figured out electron transport in graphene. The time before that, he was making a list of who’s allowed in his tree fort if he ever gets one. Still can’t believe I didn’t make the cut." This can't be true because the first event Amy is referencing occurs in "The Einstein Approximation" (Season 3 Episode 14). Sheldon is stuck on a problem which he describes as, "Trying to figure out why electrons behave as if they have no mass when traveling through a graphene sheet." Sheldon hadn't even met Amy by "The Einstein Approximation," so claiming Sheldon excluded Amy from his approved tree fort guest list is fallacious. The only justification to make it logical is that he first created the list before meeting Amy, periodically edits it, and excluded Amy up to that point.
Bernadette says at least once her mother ran an illegal daycare center so she is good with kids and how she loves kids etc. In a later episode she goes on about how bad she is with kids during Howard's magic showk and again in another episode she wants nothing to do with having a child of her own.
Note: Checkout the Goofs sections for TBBT episodes on the Internet Movie Database and the Inconsistencies page in this wikia.
