Edit: Also I am curious what bad moves in particular you are referring to in 61 and 62 (the main thing I that comes to me is allowing themselves to be provoked and attacking Ft. Sumter and doing Lincoln the favoring of letting him claim that he was just defending himself). The first major Union victories (that I can recall) of the war were in the Summer of 63 (Gettysburg Campaign and the fall of Vicksburg).
I have studied the war only rudimentary, but I believe there were a lot of strategic mistakes in the West. In particular, leaving New Orleans undefended.
In the East they had Bobby Lee, but in thew West there were many military failures because they lacked equally skilled commanders. For example Van Dorn's foolish move on St.Louis.
Then there were the many political mistakes like a failed cotton embargo, which denied them of their most important income, but did nothing to bring Britain into the war.
By 1863 it had already cost them most of Missouri, Arkansas, Mississipi and Lousiana. At the point on which the game began they had already lost half their territory in the West, with the enemy now operating along the big river, and in their heartland.
Aren't there many theories why the Confederates lost the war? One being that the whole idea of the Confederacy was faulty, too many state rights left the government powerless in times of a war. Davis demanded the same powers of administration as Lincoln but never got them. This allowed the black market economy, hunger, inflation, 2/5 of the troops being absent without leave, things that eventually killed the Confederacy. Then of course the superior economic output of the union. It is said that at the beginning of the war the whole amount of goods produced in the Confederate states being less than a fourth than the state of New York alone. Their economy depended completely on export of cotton but they did not have a navy to protect it.
Lastly, foreign recognition (and possibly later, intervention) could not come without at least partial emancipation of the slaves. I think this whole slave issue was perhaps their biggest weakness. Lincoln shrewdly exploited it by simply declaring all slaves free, as long as they were in a Confederate state. Everyone in a union state could keep their slaves. And even if the Confederate realized that they had to free the slaves to get recognition, and that they had not gone to war because many other things, they could not do it because that would have been killed by internal dissent.