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.
Factual error: In 1973 there is a Boeing 747-400, however this kind of model of 747 was not in service until 1988.
Chosen answer: Government agents were previously aware of mutants - they are probably the same ones that imprisoned Magneto, and his attempt to prevent JFK's assassination was most likely covered up due to the revelation that Kennedy was a mutant. Magneto was already in prison by the time Trask pitched his Sentinel idea to the government, which is probably why the program wasn't instituted.
Phaneron ★