Factual error: When Magneto enters RFK stadium, a groundskeeper is lining a baseball field. RFK stadium did not host baseball in 1973, as the Washington Senators had moved to Texas to become the Texas Rangers after the 1971 season. In 1973, the only team playing in RFK regularly was the Washington Redskins of the NFL. In addition, the Paris Peace Accords were signed in January of 1973; so there wouldn't be green grass inside the stadium, regardless of what sports were being played there.
Continuity mistake: Charles has just denied Logan's request for his help and is now in his bedroom. There's a photo of Raven on the right side of his bed with an ashtray slightly behind it. A couple of shots later, the ashtray is gone and the photo has moved closer to the bedside table's edge.
Revealing mistake: Logan, Charles, Erik and Hank are boarding the plane after breaking Erik out of the Pentagon. Erik goes to reach down for the paper and Logan stops him by placing his bone claws down on the paper. On the third column of the article on the front page, the article mentions a shoemaker named Max Schwartz and a couple of paragraphs below, a woman named Mrs. Locklan Smith. On the fourth column of the article, the exact same paragraphs of both the shoemaker Max Schwartz and Mrs. Locklan Smith have been repeated a second time.
Other mistake: During the final battle of the theatrical cut, in the future sequences, in at least one shot, you can see in one of the reflective surfaces of the room where Logan is being "sent back" that Rogue is the one controlling him and not Kitty. This is a remnant of a deleted sequence where Rogue is brought in to absorb and use Kitty's power after she was injured. The scene was cut from the theatrical release and the film was re-edited so that Rogue wouldn't appear in the future and Kitty is the only one "sending" Logan, but at least one shot where she's visible in a reflective surface was left in as an "easter egg" for fans. Still, it is technically a mistake in the theatrical edition. (The Rogue version of the scenes were included subsequently in the extended "Rogue Cut" of the film, and in the special features, this intentional mistake in the theatrical edition was confirmed by producers).