Erik did not help Xavier build the Cerebro located at the CIA facility. But to be honest, Xavier didn't build that one either. Beast did. It was already built when Xavier and Erik came into the picture. It's not far fetched to think that after the CIA was attacked and they retreated to the Xavier mansion, they built (began building) another Cerebro in order to continue their quest to locate and contact mutants. It stands to reason that Erik helped build the "Xavier Cerebro," seeing as how the construction would go a lot faster when you have a guy that can move metal with his mind. We also saw in X2 that Erik can manipulate Cerebro magnetically, and has enough knowledge of the way it works to be able to adjust it to target humans exclusively. So, in The first X-Men movie, when Xavier and Wolverine are inside (the mansion's) Cerebro and Xavier says to Wolverine "he (Mageneto) helped me build it," Xavier is clearly talking about the Cerebro that he was using at the moment - the one located inside the mansion - which we do not see in First Class, but can easily be shown in a flash back during "First Class 2" as being built during the events of First Class.Mister Linton said:Erik did not help Xavier build Cerebro according to FC. There, X1 is no longer cannon. Enjoy.
Like I said, all the silly fanboys need to just accept each movie as it's own story and stop worrying about continuity, the filmmakers threw that out a long time ago.
Also, in the first X-Men movie Charles states that Magneto's helmet is designed to prevent Charles reading his mind. Yes, this was clearly a revelation/new development at the time, but as far as remaining in continuity with First Class, Charles' behaviour in X-Men doesn't completely contradict what he already knew about the helmet. He could have simply been clarifying for Wolverine, the others, and the audience, that Erik's helmet is designed to block his telepathy. Charles never said anything like "I'm completely surprised by this discovery as I had no idea such a thing was possible."
As for Beast appearing human in X2, First Class makes it clear that Beast is concerned about his appearance. Raven pretty much tells him that the world should accept them as they are, and he tells her that it will never happen. Raven's last words to him were "Remember...mutant and proud!" This leads me to believe he was still at odds with his appearance. Who is to say that Beast did not continue searching for a cure for his appearance, and found it? He could have tried again and succeeded. At no point in First Class do we see a McCoy that has come to terms with his mutation.