Read Gordon C. Rhea's "Cold Harbor" - he's the acknowledged expert on the Overland Campaign of 1864, and he presents a lot of information and evidence that prior historians have completely overlooked.
First, Horace Porter's "Campaigning With Grant" led to the lie that the "soldiers knew they were going to die so they wrote their names on pieces of paper and pinned them to the backs of their shirts". This one little story accounts for 90% of the "butcher" mythology about Grant. In fact, the Union soldiers did this before any assault, and since it was something Porter hadn't seen before, he took it as a sign that the men knew it was going to fail but went anyway. Later historians, for a century now, have quoted that account of Porter's as if it were evidence that "everyone knew the assault would fail but Grant".
In fact, it's an outright lie and a complete myth, based on completely erroneous interpretation of an event.
Grant's strategy at Cold Harbor was completely sound (as Rhea points out). Lee's army had their backs to a river, were not dug in, and Grant was only seven miles from Richmond. He knew an assault had a good chance of success, and being under pressure for political reasons (the upcoming Republican convention and the upcoming election) he knew that if the assault succeeded it would end the war right then and there.
And here's something that Rhea also points out - it almost worked.
Almost only counts in horsehoes and handgrenades, I know, but what Rhea points out is that if Grant's orders had been followed immediately and the tactics hadn't been so bungled, it's very likely the Union would have destroyed Lee right there.
Unfortunately a few things happened. Meade was inept, and being in charge of the tactics, he bungled the assault from beginning to end: First, the assault got delayed for twenty-four hours, again, due to inept commanders - this gave Lee time to fortify. Second, once the assault was underway, it was totally disorganized and uncoordinated, with various divisions and brigades getting off at different times, etc, leading to a completely uncoordinated assault on the Confederate position.
Grant's mistakes were:
1. Leaving Meade in charge.
2. Not calling off the assault after it was known his orders wouldn't be followed when he ordered the assault - that they would be delayed for twenty-four hours.
3. The negotiations with Lee after the assualt that left men lying on the field for two days.
Ultimately, since Grant was in overall command, he has to bear the responsibility. But the blame isn't his, for the bungling, it's Meade's - actually, it's most of the command of the Army of the Potomac.
It's amazing to watch the performance of Grant's Army of the Tennessee in the West - the army that was imbued with Grant's "spirit" - the army he built up, the commanders he picked - and their brilliant success.
And it's depressing to seem him come east and try to manage this large, political, bungling, incompetant mess that was the Army of the Potomac. It's command was a morass of political appointees, egomaniacs, megalomaniacs, prima donnas, and intriguers.
In fact, I am often amazed that Grant was able to win the war, with the Army of the Potomac. It was a pathetic excuse for any army.
The average soldier in the AOTP cannot be faulted in most cases. But you do see a difference between the "suck it up", bold, aggressive, "can do" westerners in the Army of the Tennessee, and the whiney, moaning, soldiers in the AOTP whose morale rose and fell like the rising and setting of the Sun - and as often. They were also imbued with "McClellanism" - his spirit infected the AOTP.
And the command structure Grant was left to deal with...Oy...apart from Hancock and Sedgwick, there was almost no competant commander at the Corps, Division or Brigade level in the AOTP. None come to mind, anyway.
However, if you want to get picky, Cold Harbor was a repeat of a smaller, equally disastrous frontal assault outside of Vicksburg---I forget the exact engagement, but it was eerie how close to Cold Harbor it was. So where I would criticize Grant is for not making a mistake, but for repeating it.