What We Owe to Each Other - S1-E6
Visible crew/equipment: You can see a crew member hand Janet a stack of papers behind her back.
Continuity mistake: When Eleanor tells Chidi she loves him she has dark nail polish on. When she starts to argue with Tahani her nails don't have any polish on. As shots change during their discussion her nails keep changing colour. (00:10:50)
...Someone Like Me as a Member - S1-E9
Continuity mistake: In the flashback where Eleanor gets offered a permanent position at the company she's working for she's holding a cup of coffee on the desk in front of her. After she says "I'm good" the shot changes and she has a Rubik's Cube in her hand. The shot changes back and she's holding the coffee cup again. (00:17:10)
Other mistake: When Michael walks into his office and sees Shawn, Michael is wearing a wedding ring. Looks like he forgot to take it off prior to shooting the scene. (01:00:00)
The Snowplow - S3-E3
Factual error: When Chidi activates the superboard, one of the items under Local News is "Rep. Sackett indicted on 231 counts of fraud." Lower house members aren't referred to as Representatives in Australia, the correct title would be MP. (00:09:13)
Continuity mistake: At the beginning of the episode while Michael is talking to the Judge, he does not have a Bad Place pin on his left lapel. However, at the end of the previous episode, as he and Janet come through the portal he is wearing one. On another note, not sure how he got the pin. As Shawn was talking to Michael in episode 11, he wasn't wearing one either and Michael had given his own pin to Eleanor. (00:00:01)
Continuity mistake: The note that Eleanor pulls out in the beginning of the episode does not visually match with the one she picked up at the end of last episode.
Revealing mistake: Janet is holding a coke in her hand that she is supposed to be conjuring up but is already holding it.
Factual error: As Eleanor walks in the corridor to Chidi's office at St. John's University, there's an exit sign mounted in the ceiling above her - a North American style red Exit sign. As she is in Australia, it should either a white on green Exit sign or an international "running man" style sign, as North American style signs were never legal in Australia. (00:20:55)
Audio problem: While Accountant Steve Merchant is getting angry at Michael his words do not match his jaw motions during the shot from behind Merchant's face wherein he says "Now if you'll excuse me". (00:17:10)
Other mistake: When Michael is looking at the 2009 report about Doug giving his Grandmother flowers, the net total for the action is -4 points. But the totals are off. The positives add up to about 73 points, but just the negatives that we see are 162, making the net total at least -89. While the header implies only the "top" points are known, the numbers start tailing off drastically after the first few, so there's no way there are enough not mentioned to make up the difference, otherwise they'd be classified as "top" too.
Answer: No, he is fictional. The joke is that, despite being handsome and charming, Larry Hemsworth is so overshadowed by his brothers that nobody else has heard of him and he feels like a failure.