I'm going to add a slightly unconventional answer. It's not a weapon, though those added to the horror. It's not a tactic, though using Napoleonic tactics with more modern weaponry surely affected the casualty rates. It’s not the bitterness of brother against brother, though that surely contributed.

It's railroads.

Railroads were a critical component of the American Civil War. While there were logistical geniuses in the past (Napoleon comes to mind), the contributions of railroads to the battles during the war were relatively novel. The ability to deliver men and heavy loads of supplies over long distances and in any weather was still a fairly new concept.

By making use of innovations in communications, weaponry, and transport, principally the railroads, the belligerents, especially the North, developed a new type of war that was fought with much wider use of technology and in a way that relied on mobility and flexibility than its predecessors. (Christian Wolmar, Engines of War, pg 34)

In short, the American Civil War was an industrial war, and perhaps even "the first industrial war."

Also, before the war started Americans were fairly profligate in their building of railroads. “By 1840 there were 2,818 miles of line and at the end of the 1850’s a total of 30,000 miles, more than the rest of the world put together.” (Wolmar, pg 35) Despite the conflict ranging over an area the size of Europe, the density of railroad lines made combat more intense in some areas and elevated it to possible in others. In the western theater of the war, many times the railroad was what made combat feasible on any kind of scale.

So, how did railroads make the US Civil War so bloody? In the eastern theater, the contribution of the railroads made for more intense combat than could have otherwise been sustained. Previously, supplying an army in the field was a tenuous affair. Napoleon, known for his genius in maneuvering large numbers of soldiers to converge on a single location to overwhelm his enemies, used everything at his disposal to supply his men. This included the traditional wagon trains, and was supplemented with extensive foraging by his men while en route. Despite his genius for organization, Napoleon would likely have been astounded by the advances railroads made in the realm of logistics. Wagon trains and foragers could be hampered by weather. Even a moderate rainfall could turn some roads into a muddy morass—a problem still suffered by US Civil War troops. Also, going over the same area with a large volume of either troops or wagons would reduce the efficiency of those units. This is because once an area has been picked over by troops, it logically holds fewer resources for troops in the immediate future. Wagons in your supply train going over the same road could wear down a road in short order, and if the road was not upgraded from a dirt track it could be destroyed by traffic.

Railroads changed all of this. There was little diminution of effectiveness relative to use of the road, with the biggest limit being the total number of cars you could haul per day—not the wear and tear on the track. Also, railroads could deliver their loads in most any weather condition. Though they were not completely immune to changing meteorological conditions, locomotives were much more resilient than wagon trains. Finally, the sheer amount of supplies a railroad could deliver was astonishing. As a result, armies in the eastern theater could grow in size to quite large proportions, and could be supplied in near perpetuity. With larger armies, larger casualties were a frequent result.

The most fundamental lesson of the use of railways in the Civil War was, of course, the sheer logistical advantage which they offered...the railroads enabled armies to be bigger and to be supplied from bases much further away than previously. (Wolmar, pg 60)

In the west, there were times that railroads made combat possible beyond simple cavalry raids. One vivid example are the battles of Chickamauga and Chattanooga. First, two divisions of General Longstreet’s Confederate troops were moved from the eastern theater to the west. Not only was this large scale movement of troops only possible with railroads, but supplying them in the field was also only possible with the support of rail lines. While the Confederates were able to use mobility and logistics from their railroads to win at Chickamauga, the Union was even more successful in reinforcing and supplying their forces in Chattanooga. The eventual result was a Union victory, but the battles were only truly possible because the railroads could deliver the men and material into position to even have the battles in the first place.

Certainly the efficiency of the supply lines made possible by the railroads increased the intensity and length of the war. Not only did they allow both sides to build up and maintain far larger troop concentrations than ever before, but they obviated the need for foraging by armies. In much of the Western Theater, there was no agricultural development which would have allowed armies to live off the land in that way and therefore it was only thanks to the railroad supply lines that battles could take place there. Thus the railroad made it possible for more frequent and intense offensives to be launched during a war, but an unexpected consequence was that the railroads made it more difficult for an outright winner to emerge from these battles because losing armies either could be resupplied more easily or they could cut and run. (Wolmar, pg 62)

In all theaters of the war, railroads ensured that you could move men on the defensive more rapidly than the attacker. As soon as you could ascertain the enemy’s movement, your trains could move troops and material far faster than a man’s walking pace, which would allow you to adjust your defense to meet them. As a result, defeating an opponent in detail by “stealing a march” became much more difficult to pull off. The same tricks could be pulled by the attacker to gain an advantage—screening your march, forced marches, diversions—but as soon as the enemy figured out your location the railroad would let them move much more quickly. Since the defender could reinforce and reposition, a more intense defense could be mounted.

There were limits to this kind of warfare, though. As soon as you moved away from the railroad—your “railhead”—you immediately had the same issues as every other army going back through recorded history. You were confined to whatever you could scrounge on the way or carry with you in your wagon train. The same went for any area within range of your enemy’s guns, as you couldn’t risk your locomotives and rolling stock to enemy fire. In a way, the railroads placed restrictions on army movements. Once you became accustomed to using them, doing without could be difficult. As a result, you end up largely tethered to your rail network, with moving away from it being seen as a fairly large risk, when a couple decades before it would have been seen as the norm.

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Now, I am not arguing that other factors did not increase the bloodiness of the conflict. Rifled muskets with massive bullets were terrifying weapons of war. Linear battle using Jomini’s tactics with those much more accurate weapons than Jomini could dream of was also a contributing factor. The very fact of it being a civil war likely contributed to the bloodshed. But one of the factors that was different than previous wars was the railroad. Wolmar is quick to point out that the American Civil War was not the first usage of railroads in war, with the Crimean War being one of a number of earlier usages. However, the extent of the usage of railroads during the US Civil War was impressive. Industrial war was the result, and the ability of the railroad to deliver men and supplies to the battlefield certainly contributed to the horrendous casualties of that conflict.

(edited to add more quotes)

It lasted so long because the intense differences over slavery and state's rights finally came to the brink and went over it after everyone had tried to ignore it. The South would not give up power to a pro-abolitionist government that would threaten to increase the powers of the National Government, while many in the North would not tolerate slavery, and many others would not tolerate the dissolution of the union. With both sides so willing to fight over the issue, solving the problem would never be short.

This was proved after the First Battle of Bull Run. The Confederates won the battle and assumed the North would surrender after losing so much men. Instead they recovered. The Union victory at Shiloh also proved that the Union army could fight hard too, further proving that so long as both sides refused to "give" on the issues at hand, the war would continue. It took four years of bloody fighting and the absolute destruction of Southern land and property and most importantly, their economy before Lee finally surrendered at Appomattox Court House, ending the Civil War, and making Jefferson Davis a President without a country.

Why was the Civil War so deadly among all American wars? Many reasons. One, no matter you spin it, every casualty in the Civil War was an American. The total death tolls of the World Wars is much higher, but is divided among many different nations (although some suffered more then others), but every man killed, wounded or captured in the Civil War was an American. With only one "nation" fighting, the casualties recorded in that nation's military history will be higher.

Second, was the advancement of technology during the Civil War. The Springfield and Enfield Rifles used by the Union and the Confederacy had a greater range then their Revolutionary War predecessors. They were also far more accurate, which made them far deadlier. Civil War artillery was far more accurate. And as the war the progressed, newer weapons were created. The Gatling Gun was patented, a forerunner of the modern machine gun. Breach loading repeating rifles, forerunners modern bolt action rifles and assault rifles, saw active service from 1864 on. The ironclad warship appeared in 1862.

Yet on both side, tactics did not change. The deadlier weaponry made the Napoleonic tactics used by the North and South to be obsolete. Using inferior tactics and superior weaponry insures heavy casualties. Europe would learn the same lesson in World War I.

The North won in the end because it had more men and material to fight the war then Confederacy. Grant, Sherman, and Sheriden were good commanders, and Meade was decent, but none of them ever put forward a strategy that Lee couldn't outthink. Grant eventually beat Lee by forcing Lee to fight battle after battle, until Lee couldn't replace the men he lost.

The result of the Civil War was that America was a singular nation with supreme power vested in Washington DC, not in the individual state capitals, and that slavery wasn't legal and could not be defended.

One argument I've always found fascinating is that the Civil War was actually much less deadly (or "bloody" as you refer to it) than it could have been.

Within a few short years game-changing World War I technologies start getting invented. Barbed wire, modern artillery, machine guns, bolt-action rifles, air force, tanks, and even poison gas are all things that a Civil War soldier never had to deal with.

Had the Civil War been fought with World War I technology, the casualties would have almost certainly been in the millions rather than the hundreds of thousands it ended up being.