The battle of Fredericksburg.

I assume the accident is referring to the late arrival of the pontoon bridges, which prevented the Army of the Potomac from crossing the Rappahannock before Lee's army was dug in at Fredericksburg.

The initial plan of attack was to focus on the Rebel right(?) on Prospect Hill, but due to poor coordination and lack of initiative by "Grand Division" commander Franklin, the attack bogged down after initial success, and eventually the focus of the attack shifted to Marye's Heights (initially intended as a "diversion") with disastrous results.

Simply put, Lee's army was probably too strongly entrenched, with huge advantages in high ground, earthworks, and interior lines, to permit a Federal success. Burnside's strategy of launching attack after attack was begging for disaster, and pretty much doomed to failure. Victory wasn't impossible if Burnside had done a better job of coordinating his assaults, but he didn't and the result was a one-sided defeat.

Sedgwick did capture Marye's Heights during the Chancellorsville Campaign, but keep in mind he was dealing with a much-smaller Confederate force.

"PLEASE DON'T DATE ME! I PROMISE I'LL WORK HARDER!"

This is a well-done representation of half the battle. As Hancock the Superb writes, the initial attack was on the Confederate Right at Prospect Hill; one young Artillery commander with one gun kept the Union at bay for most of the day. When the Union nearly broke through, Jackson moved troops and stopped them.
The weather was so cold men froze to death on picket duty, and contrary to what a number of people have written in posts on this site, the northern lights were visible on one night.
The "accident" as Hancock writes, was totally a political smoothing-over of something which should never have been allowed to take place.

Burnside sent those divisions straight across open ground to attack an entrenched position, the same mistake Lee made at Gettysburg.