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)
Don't Let the Good Life Pass You By - S3-E8
Plot hole: When Janet and Michael visit Doug Forcett, they realise his lifestyle, like drinking his own urine and only eating lentils and radishes, is not the "blueprint" they imagined. However, Janet should already have known all of these details, due to knowing everything about everyone in the universe, so a) she could have told Michael this without visiting Doug, and b) she should not have been learning all this for the first time herself.
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.