Not to mention a greater confidence in the medical services by the frontline. Most doctors, surgeons and 'medics' of back then were very poorly trained or completely ignorant of the medical practice. Sort of just 'well my daddy was a pretty good healer-' 'You're in!' and so had to use a lot of 'common sense' to help the poor souls. So if you were on the front line and got a shot anywhere crucial, you were as sure as dead. So to improve the medical services:
-a greater number of experienced doctors and surgeons (for rural areas this would be hard because a lot of towns and villages only had one doctor to rely on)
-a greater number of experienced 'medics'. For a week after First Manassas you had wounded still unattended on the battlefield and this was repeated constantly. Most of these guys didn't understand that it was essential to treat the wound ASAP and just took them back to the tents to die or the long bumpy road to Richmond/Washington.
-More hospitals. Except for some truly magnificent hospitals in some places (CS I know had huge ones in Atlanta and Richmond that were excellent by 1860's standards: heating, food, etc.). Authorities usually largely underestimated battle casaulties: in Washington '64 wounded Yankees were found lying in the streets, bars and even Congress because the hospitals couldn't cope. More staff at these hospitals too: most had only 1 doctor and a dozen nurses to care for 1000's.
-more proper tools, equipment and medicine. Alot of surgeons followed 'common sense' and home remedies when renowned medicine and treatments ran out. A better knowledge of cleanliness would drastically reduce deaths.
-better food, more of it and better cooking knowledge. Early in the war alot of soldiers had heaps of food - but didn't know how to cook it properly, most suffering from food poisoning. As the war dragged on, the men got wiser but the food got worse. The US had HEAPS of food...but it was mainly just pickled pork, hardtack, bacon and coffee. This bland diet with no vitamins or healthy stuff made soldiers weaker and have a greater chance of infection. (In Georgia '64 there were often battles just for berry bushes such was the crave for better food).
So what would this mean? You probably wouldn't have the insane 1/4 dead to disease rate. More vigorous armies, a greater confidence in those behind the line perhaps. Armies may become slower in the first years of the war (some POD's there maybe) but by the grinding years of late 63-65 this wouldn't have been a problem. Maybe the best thing to come out of it would be not as many good young men dying and a greater start for medical services for wars in the 20th century.