When I first started playing, I thought the Civil War was interesting and the game seemed to be a nice strategy game with a different angle. I've since read a ton and now consider myself a bit of a buff of the era, so I've learned a lot of things during the time that I've been playing the game. But I've learned a few things from the game specifically, some true and some false, and I was wondering what the game teaches that I've missed. Another way of thinking of this list is here are some big picture facts that are true in the game and in real life. Many of you will have known this before playing the game, of course.
First, I learned the names of a lot of generals and have a rough idea of who was considered good and bad and of when they were promoted. Some of these things I've learned might not be true, particularly the timings of promotions.
I've learned a bit about the relative contributions of states to the war - particularly the enormous numbers of regiments from NY, PA, OH, and IN (I don't play CSA often enough to have a feel for it on that side).
I've learned that marching an army through heavy mud is a terrible idea, even though walking through mud as an individual can be manageable.
I've learned that having the regular army in the far west meant that the Union had a hard time securing federal property, from West Texas to Harpers Ferry and Gosport, all of which quickly fell into Confederate hands.
I learned that Norfolk was the key to the Confederacy's navy in the east, mostly because of the Merrimack.
I learned that blockade running was easy but not that valuable to the Confederacy overall. The Confederacy's cotton also didn't provide a large windfall to their war economy.
I think the biggest thing I learned and the reason the game is good is that the war was very influenced by geographies: the Missouri and Shenandoah Valleys, the vastness of Indian Territory, Texas, New Mexico and Arizona, the mountains of eastern Kentucky and Tennessee, the swamps on the coasts, possible and impossible paths of invasion and retreat, etc. In the game, there are very few impassable regions in good weather, but there are tradeoffs, bad weather, supply, and cohesion considerations in movement which make for a very cool feel to the game.
There are a number of things the game abstracts very heavily or even misses on, particularly the variety of artillery and navy, how cavalry can and can't be used, water crossing, naval landings, internal and external politics, slavery, the role of state militias, etc. Some of these could be fixed in mods, some could be fixed by the devs, and some are impossible.