When MLK starts to address the SNCC for the first time, Abernathy's position changes in the first two shots.
In an early scene, MLK wears a tie with a tie bar. The position of the tie bar changes three times.
When MLK meets with LBJ in the Oval Office, Johnson is seated at the Resolute Desk. When Lyndon B. Johnson took office in 1963, he found he was too large for the desk, and commissioned a plainer replacement which was built by the Senate cabinet shop.
Sheriff Jim Clark was not on horseback firing a pistol during the first attempted march to Montgomery. He had just flown into Montgomery after an appearance on ABC's Issues and Answers (1960) and arrived about the time the march broke up.
President Johnson is shown giving the voting rights speech in front of what appears to be the the Senate (individual desks shown) with the Speaker of the House and the Vice President behind him. This speech was given properly in front of the joint session in the House chamber (which has just seats rather than desks). The room depicted isn't correct for the Senate chamber either. Neither chamber has windows as shown.
Alabama State Troopers in uniform have never worn facial hair.
One scene depicted as being in 1965 has a 1967 Thunderbird visible in traffic.
When MLK goes for a drive with John Lewis to talk, the movement of the steering wheel doesn't always match the movement of the view out of the windows, especially when cornering.
The movie takes place in March, but it was filmed in the middle of a hot Summer. When the marchers are walking over the bridge, you can see crepe myrtles blooming.
MLK replaces a transparent plastic trash bag. In 1965, home garbage cans were lined with a paper shopping bag, if at all.
When MLK leads the marchers across the Edmund Pettus Bridge, a cell phone tower is visible on the right side of the screen.
As the first march to Montgomery begins, an establishing shot shows a sign with an italicized Pepsi logo introduced in 1991.
Toward end of the movie, a white man sits at a table smoking a cigarette. A plastic bottle of Fiji water is on the right side of the table.
In an early scene in the Kings' kitchen, a blender is plugged into a grounded GFCI outlet with a bright green LED. Those technologies were not commonly available until the 1970s.
A note at the end of the end credits thanks the cities of Covington, Conyers, and Marietta, Alabama. Those cities are in Georgia, not Alabama. Montgomery and Selma were the only Alabama filming locations.
The film has King stopping the second march (Turn Around Tuesday) on top of the bridge and kneeling. King actually took the marchers further on to HWY 80 & King's Bend Rd where he knelt and tuned the march around.
The FBI data shown on the screen says that Martin Luther King arrived in a Selma hotel at 10:24 AM. A few seconds later he walks in and says "Good afternoon."