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.
Category 55 Emergency Doomsday Crisis - S1-E5
Visible crew/equipment: A crew member and their boom mic are reflected in one of the windows in Eleanor's house as she and Chidi pretend to go to bed. (00:19:30)
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.
...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)
...Someone Like Me as a Member - S1-E9
Continuity mistake: When teenaged Eleanor stands on the table to make an announcement, she dumps food on the table. In the next shot the food has moved.
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)
Audio problem: When Janet is talking to Michael about how she loves Jason, there is a shot looking at Michael with Janet to the right. Janet is talking but her lips aren't moving.
Continuity mistake: The strap on Tahani's right shoulder drops during the scene where she is talking to her soulmate about how to dress. When Michael is there, it is up on her shoulder. At the end of the scene it is down.
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)
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)
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)
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)
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.
Revealing mistake: Janet is holding a coke in her hand that she is supposed to be conjuring up but is already holding it.
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.