History

the other thing that happened 150 years ago was the surrender of the Confederate forces in Vicksburg, Mississippi to Grant, after a brilliant campaign. Vicksburg would have a number of effects:

• Grant's reputation would be cemented, leading to his becoming General in Chief


• The Confederacy would be cut in half as the Federals regained control over the Mississippi River


• Federal commerce on the Mississippi would be restored

It is hard to over emphasize the impact of this victory, which is overshadowed by the fact that Gettysburg happened at the same time. Grant would go on to fix the situation at Chattanooga that had resulted from Rosecran's bad day during the Chickamauga campaign before heading east. And Grant was the first commander in chief to truly understand what would be needed to end the war.
Grant had intended to command from the west, but after taking command, he would decide to place Sherman, his most trusted subordinate, in command in the west, while he shadowed Meade & The Army of the Potomac.

150 years ago today - the day after the battle
First, some things missing from the film
I already talked about day 1. For day 2, the film focuses almost entirely on Joshua Chamberlain and the 20th Maine on Little Round Top. So what's missing? Well, lots.
Chamberlain's Regiment was part of Strong Vincent's Brigade. Vincent's Brigade was rushed in to cover Little Round Top after General Warren discovered it was uncovered and that the Confederates had figured that out. All the regiments in Vincent's Brigade were heavily involved, and Vincent himself was killed that day. Now why was Little Round Top uncovered? Because General Dan Sickles had ignored instructions and moved his forces forward from Cemetery Ridge to the Peach Orchard and the Wheatfield. Sickle's forces were not sufficient to extend to Little Round Top, so they were anchored on Devil's Den. There was intensive fighting in the Peach Orchard, the Wheatfield and Devil's Den, none of which is covered in the film. And the film doesn't cover any of the fighting going north along the line, wrapping around Cemetery Hill and Culp's Hill.
Day 3 in the film is all about Pickett's charge, but ignores all kinds of other fighting that day.
Context
Generally missing from most Gettysburg discussion (film or otherwise) is context. Meade is often criticized for failure to pursue, but actually the Army of the Potomac followed Lee for 10 days, almost trapping Lee against the Potomac River. Meade seems to have come up about one day short on catching Lee, but Lee's escape wasn't exactly a cakewalk.
Some recommended books
Gettysburg: The Last Invasion Allen C. Guelzo
Gettysburg Stephen W. Sears
Plenty of Blame to Go Around: Jeb Stuart's Controversial Ride to Gettysburg Wittenberg & Petruzzi
One Continuous Fight: The Retreat from Gettysburg and the Pursuit of Lee's Army of Northern Virginia, July 4 - 14, 1863 Wittenberg, Petruzzi & Nugent
Protecting the Flank at Gettysburg: The Battles for Brinkerhoff's Ridge and East Cavalry Field, July 2 -3, 1863 Eric Wittenberg
Gettysburg's Forgotten Cavalry Actions: Farnsworth's Charge, South Cavalry Field, and the Battle of Fairfield, July 3, 1863 Eric Wittenberg

Most of the focus will be on a small town in South Central Pennsylvania. What happened there is significant and fascinating, but generally it is overemphasized at the expense of the real action.
In the western theater, forces under General Grant had successfully executed his novel campaign plan, with the result that he had Confederate forces under siege in Vicksburg Mississippi, and the Confederacy was about to be split in two as the Federal government gained complete control over the Mississippi River. Arguably this was far more important to the course of the war than what happened at Gettysburg.
Vicksburg
By July 1st, Grant's brilliant campaign had settled into a siege. The defenders of Vicksburg had no way out and it was only a matter of time until they ran out of supplies. This moment would be coming soon. In addition to splitting the Confederacy, Grant & Sherman would also start to set a pattern for future operations that would carry through Sherman's march through Georgia in 1865. The pattern? Unable to occupy Jackson Mississippi, Grant would send Sherman to raid Jackson instead, and Sherman would destroy the railroads, the warehouses and the factories, leaving nothing in Jackson of value to the Confederacy.
Gettysburg
The events of the first day are only partly described in the film. The film omits entirely the intense fighting on the west side of the town which lasted until the two Federal Corps were overwhelmed by Confederates coming from the west and the north. The Federal forces would stream through the town and settle on Cemetery Hill, where the remainder of the Army of the Potomac would arrive for the second day's battle.