Base-Breaking Character: John can easily be seen as this, with the majority of the tropes on this page focusing on his errors and numerous take thats, which some find more insulting than funny. His laser-like focus on social history can either be a unique perspective not shown in normal history classes, a worthy addition but given too much focus, irritating because he tends to say the same thing over and over and, or end up being really insulting.
The episode "Battles of the Civil War" has proven to be this. Some viewers accepted John's basic listing of major battles of the Civil War as a good Take That, Audience! towards those who ask for more military history on the show and acceptable filler to pad out his paternity leave, especially since the following two episodes were also about the Civil War and contained much more analysis and details. Others dislike the episode, either because they see it as disrespectfully trivializing the entire field of military history and/or because an intentionally boring episode is still boring. On a specific note, confidently claiming that military history focuses on battles and *doesn't* go into logistics, politics and the experience of the common soldier is really baffling for anyone who took any interest in military history beyond the high school \ internet hobby level.
The 2016 series on Games has spawned criticism of its chronological order and prioritization of topics. First, the decision to skip directly from ancient board games to the advent of video games was met with some criticism, because it ignores a lot of the evolution of board gaming, card games, tabletop games like D&D, and how these all connect to each other. Then, to further break the fanbase, the series focused heavily on consoles over PCs, causing a number of fan debates over what is important in terms of video game history. While the series are now focusing more on those subjects, the fact that the subjects aren't going to be handled in chronological order is a little jarring to quite a few viewers.
Squick: Episode 4 of Crash Course Psychology shows us what happened to Phineas Gage, a man who had a railroad spike go all the way through his head.
Woobie: John Green would probably disagree, but after she's beaten around for an entire Crash Course: World History, it's totally reasonable to feel a little sorry for John's college girlfriend.
Tropes from the TV Series
Paranoia Fuel: Flipping a car onto its roof and being stuck inside. Even with reinforced cars, protective gear, and paramedics on standby... that's still going to be terrifying.
Squick: Siblings that were constantly hugging and rather... touchy-feely.
One contestant called his mother "baby". Repeatedly.
Orlando (to contestant) Did you just call your mother "baby"? Contestant: I'm just getting hyped up, baby! Orlando (to Dan): Did he just call me "baby"??
