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.
Factual error: Charles, Eric, Logan and Hank are seen flying in a Gulfstream II, tail number N540EA. This aircraft was manufactured in 1975. It didn't exist in 1973.
Factual error: The Mountain Dew logo seen in the stadium didn't come out until 1980, despite the film being set in 1973. The changes made in 1980 were subtle, but still distinct, especially the loss of the "wave" in the "D" and the smaller hole on the "a."
Factual error: Major William Stryker is shown in uniform with a Silver Star ribbon and V clasp. V (For valor) clasps are not awarded with the Silver Star.
Factual error: In the aerial shot of the Pentagon the caption reads "Washington, D.C." The Pentagon is in Arlington County, Virginia, across the Potomac River from Washington, D.C.
Continuity mistake: When Quicksilver duct tapes the guard in the elevator, the tape changes when Quicksilver and Magneto come back. For example, when they get back, the tape on the chin is now tucked under tape strips and there are more spaces seen.
Factual error: In 1973 there is a Boeing 747-400, however this kind of model of 747 was not in service until 1988.
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. (00:33:50)
Other 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. (00:52:20)
Continuity mistake: Logan has just woken up in the past. In the first shot of him, the blanket is nowhere to be seen. In the next shot, the blanket now covers his stomach. (00:17:40)
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).
Continuity mistake: Blink's boots change between three styles throughout the whole movie. They change between combat boots with low heels, combat boots with very high heels, and combat boots with medium-height wedges, depending on how much she is moving around in the particular shot.
Answer: If you're referring to the behind-the-head headphones, NO! They were introduced in 1997: http://coolmaterial.com/roundup/history-of-headphones/.