Nonetheless the murdering of enemy soldiers who had surrendered was considered a "no go" at the time already (as early as 1415 the murdering of prisoners of war who had previously surrendered and laid down arms during the battle of Agincourt was considered a... well they didn't use the word crime, but that's what it comes down to).
On the other hand, the prisoner of war camps were very similar to the Concentration Camps, especially with the brutality and mortality rates. I saw a picture of a Union prisoner of war soldier that if you showed to someone, they would think it was from world war II.
True, but for the sake of completeness one should point out that the treatment of prisoners was not a source of glory for either of the two parties in the war. The commander of the most notorious confederate prison camp Andersonville was the only person to be tried and executed for his activities during the civil war after the end of the war. Critics say that the fact that this commander, Henry Wirtz was Swiss born rather than born in America played a role and that he was incompetent but not deliberately sadist (as often claimed). In the later phases of the war rations in the prisoncamps in the south were horribly small, but the picture would be incomplete without pointing out that the rations of the guards weren't any higher. Many prisoners enclosed in a very narrow space with only a tiny poluted water stream in the camp were a breeding ground for diseases (which took about twice as many lives as combat did during the Civil War). About 13 000 of 45 000 northern prisoners (some 28%) died in Andersonville which was but one out of several (Libby prison in the confederate capital Richmond was another notorious one).
Unfortunately the situation was not much more glorious in many of the northern prison camps either. The deathrate at Elmira Prison / NY also was about 25% because of a combination of malnutrition (though food would have been available in larger quantities there) and coldness.
During the first years of the war prisoners had often been paroled or exchanged (there were exchange rates about how many common soldiers were to be released for a general and stuff like that). However, after the proclamation of emancipation and the setting up of African Americans Regiments the South refused to let African American soldiers be part of that prisoner exchange program (since it would have constituted a de facto recognition of their freedom) while Lincoln was consequent enough to insist on his black soldiers to be included. Since no agreement was reached about this the exchanging stopped entirely and prison camps started to become notorious from 1863 on. Concerning African Americans there had been the threat on the part of the South of turning every African American prisoner into a slave again and and executing any white officer in command of African American troops as an agitator who incited slave revolts. The second half of that threat in particular did not become official policy in the South after all, but it is rather safe to assume that Lincoln't threat of executing a southern officer for any northern officer executed played a large role in this.
Sherman's march to the sea and Sheridan's valley campaigns are not war crimes, but campaigns to end the war, similar to the bombings of Germany and Japan during World War II
For the sake of completeness it should be mentioned that there had been plenty of individual cases of civilians being murdered or raped that were not very harshly persecuted and that would by our definitions constitute war crimes.
The list of war crimes in the civil war is interesting, but if fails to mention the probably largest of all. The largest prisoner massacre during the Civil War is something of a taboo topic in many discourses, probably because it was not committed somewhere far west by some ragtag guerilla force, but by Robert E. Lee's celebrated army of Northern Virginia. During the Siege of Petersburg in 1864 a mine was used to blow up part of the Southern fortifications. The following northern attack was a disaster since in a last minute change the black troops who general Burnside had planned to lead the attack (and who had been specifically trained and instructed for this) were exchanged for unprepared white units under the command of very incompetent officers (one of whom lay drunk in his tent during the battle and was therefore dishonorably discharged). The reason for this change was that the black troops were deemed too green by Army of the Potomac commander George Gordon Meade and for Ulysses S. Grant there was also the fear of standing accused of using black troops as canonfodder in case the attack failed. The last minute change ensured the failure however since the unprepared white troops didn't charge past the crater to widen the breach but rather descended into the crater all fascinated by the spectacular sight. Southern troops rallied and under the command of William Mahone charged the crater totally defeating the federal troops at the bottom of that pit. The black troops had been sent in too but couldn't turn the tide anymore. Many northerners surrendered but the southerners refused to take any black prisoners and started shooting and bayonetting them. White federal troops, in fear of being killed themselves started killing their own black comrades in an attempt to send a kind of "we don't like them either; please don't kill us" kind of message to the southern soldiers. The resulting massacre was the largest prisoner massacre of the entire war.
When in 2003 the Civil War movie "Cold Mountain" was made (the book version of which is much more detailed about war crimes) they started out with a scene about the battle of the crater (since blowing up a fort makes for a very spectacular movie scene) they also do show black soldiers (and a Native American on the side of the South; apparently as a kind of ballance), but they don't show the massacre. In a cut scene on the DvD of the movie one wounded black soldier crawling on the ground after the battle was shown getting shot by a white soldier, but that was it. The topic is still a taboo in the south.
If you are interested in war crimes during the Civil War I very much recommend the book: "Confederate Rage, Yankee Wrath - No quarter in the Civil War" by George S. Burkhardt to you. It gives a very detailed and thorough account of crimes committed on both sides and quotes many sources.