@Tosk: Aside from the already-mentioned incongruency of a President in TLS who is far too old based on official dating, the only other issues that aren't covered by retcons have to do with props, and are as follows:
* Wolverine has his iconic banded leather jacket in First Class and DoFP even though he doesn't actually get it until the events of Origins: Wolverine, which take place much later
* Josh Helman's William Stryker is missing his commendation service medals from the Korean War during his appearances in DoFP
Most of the things that people claim as continuity errors (Xavier walking in O:W and the flashback in TLS, young!Emma in O:W, Charles and Raven and Logan and Victor's familial relationships not being mentioned in the original X-Trilogy, Xavier not meeting Erik at 17 years of age) aren't actually errors at all because they are either covered by "word of God" statements or are retcons (and therefore do not constitute errors).