While Young Sheldon has contradicted The Big Bang Theory's canon plenty of times, the show's strangest inconsistency has shown up three times over its six seasons. Like most sitcom spinoffs, Young Sheldon has been known to bend the canon of its predecessor whenever it is convenient. In The Big Bang Theory, Sheldon often complained that his father was a drunken lout whereas, in Young Sheldon, George Sr is a sweet, caring everyman who isn't even overly fond of drinking. However, since it wouldn't be much fun to watch a light-hearted sitcom about a child-prodigy son struggling with his father's drinking problem, these changes are usually understandable.
Similarly, Young Sheldon dropping The Big Bang Theory's dark running gag about Sheldon's childhood bullying also adds up. Sheldon recounting his childhood was funny in The Big Bang Theory, but seeing a child get mistreated by his peers in Young Sheldon would just be bleak and unfunny. However, sometimes inconsistencies arise between the two shows that don't have any easy explanation. In Young Sheldon, Sheldon's beloved Meemaw is a rebellious firebrand who couldn't be less like his conservative, religious mother. However, in The Big Bang Theory, Meemaw is effectively depicted as an older version of Mary. This still isn't the most egregious discord between the two shows.
On three separate occasions, three different actors appeared as unrelated characters in both Young Sheldon and The Big Bang Theory. Despite the fact that both shows are pretty successful and, as such, could have cast any number of stars in these roles, they somehow ended up picking the same actors for two parts separate across the shows. Young Sheldon's best choice was dropping the formula of The Big Bang Theory, but the series still ended up sharing three stars with its predecessor. The earliest instance of this occurring dates back to Young Sheldon's pilot episode, since one of the main characters appeared in the earlier show.
In the most notable instance of both shows sharing an actor, George Sr's actor, Lance Barber, famously played Leonard's penitent bully before getting the role of Sheldon's father. In The Big Bang Theory season 5, episode 11, "The Speckerman Recurrence," Barber played the role of Jimmy Speckerman, a bully who tormented Leonard throughout his childhood and adolescence. Although Jimmy is initially portrayed as a surprisingly sympathetic figure, he shows his true colors by the end of the episode when Leonard finally pushes him out of his apartment and the series at large. Seven years after this episode aired, Young Sheldon expanded The Big Bang Theory's universe with Barber's George Sr.
Even though Barber's appearance on both shows creates an obvious internal paradox, this was still somehow not the only time that The Big Bang Theory and Young Sheldon shared an actor. Actor Melissa Tang played Mandy Chow in The Big Bang Theory season 9, episode 1, "The Matrimonial Momentum." Tang's role was relatively substantial since she was the girl whom Leonard kissed while on his North Seas expedition. This worried Penny and almost ended her engagement to Leonard before it was revealed that this kiss barely made an impression on Mandy herself. Mandy reappeared in the next episode, "The Separation Oscillation," before disappearing from the show for good.
Tang, however, wasn't done with the sitcom franchise quite yet. The actor appeared in Young Sheldon season 1, episode 1, "Pilot," as the music teacher Ms. Fenley. Fenley encouraged Sheldon to pursue music since he had perfect pitch. This was long beforeYoung Sheldon abandoned its original premise, so many of the show's jokes were still centered on the title character's status as a child prodigy living in a small rural town. Later on, Ms. Fenley reappeared in season 2, episode 17, "Albert Einstein and the Story of Another Mary." Here, it was Sheldon who sought her out when he wanted to learn the violin to emulate Albert Einstein.
Finally, Penn and Teller's silent half appeared on both shows, although he had a far larger role in The Big Bang Theory. In that hit, Penn played Amy Farrah Fowler's largely silent father. The famous magician appeared as Larry Fowler in numerous appearances on the show, but he also had a much smaller role in the Young Sheldon season 5 finale. In season 5, episode 22, "A Clogged Pore, A Little Spanish, and the Future," Teller played the pus in Sheldon's pimple (his partner Penn played the pimple itself). Thus, the actor became the third of three stars to appear in separate The Big Bang Theory and Young Sheldon roles without explanation.