Mass graves on battlefields were the norm, not the exception. There were burial trenches at every battlefield, some of which lost and not relocated until nearly a century later. Such trenches were found at Pilot Knob, MO and Pea Ridge, AR. It wouldn't be until WWII that the grave's registration service would do a more methodical job of interring the dead. Nor are such mass burials unique to America. The slain at Culloden were buried in mass graves and just a few years ago a mass grave of Napoleon's veterans was found in Russia. Anybody that claims their dead were "dishonored" by being in a mass grave on a battlefield is laboring under a romantic notion of funerary practices and is completely clueless about the realities of war.
In the case of the assault on Battery Wagner, there were over 250 dead laying on a beach in South Carolina in late July - they needed to be buried FAST. White troops as well as black were buried in mass graves in front of Wagner. Losses among the Union officers was particularly heavy, and they seem to have been buried with their troops. The Confederate dead, except for the officers, were buried behind Wagner.
As for Shaw, there is some debate as to the circumstances of his burial. According to a U.S. Navy surgeon named John T. Luck, he discussed the disposition of Shaw's body w/ Gen. Hagood, CSA, who said "I shall bury him in a common grave with the Negroes that fell with him." By the time the Northern press got ahold of the story, the line had morphed into "I buried him with his n----s." Hagood later denied having any such conversation or giving any orders about disposition of the dead. However, Colonel George Harrison of the 32nd Georgia reported that it was decided to return all bodies asked for except Shaw's because of bitterness over his leading black troops. Harrison oversaw Shaw's burial.
More interesting is the fate of the prisoners from the 54th. Beauregard at first tried to treat them as, albeit segregated, prisoners of war. But the governor of South Carolina demanded that they be turned over to the civil authorities for trial. Under South Carolina law, there was no such thing as black soldiers, they were either free blacks inciting revolt or slaves in rebellion. Although some of the prisoners were former slaves, none were from South Carolina. Beauregard realized that Confederate policy regarding black troops would have to change because, if put into effect, it would unleash a retalitory bloodbath. The Richmond government ordered the prisoners turned over for trial, but Beauregard made sure his aide monitored the proceedings and obtained defense counsel for the accused. They were represented by Nelson Mitchell and Edward McCrady, who argued that although the defendants had been born slaves, they were now legitimate soldiers of the United States protected by the rules of war and that the civil court was without jurisdiction to try them. Following a three day trial, the court agreed and dismissed the case. The prisoners were remanded to military custody as prisoners of war. Thus was ended the issue of whether or not the blacks were soldiers. However the question of their exchange as prisoners still remained.
For a detailed account of all of this see Stephen R. Wise, "Gate of Hell: Campaign for Charleston Harbor, 1863," (University of South Carolina Press, 1994).