Yes, an island really did disappear off the Yucatan peninsula. September 2009:
The mystery has come to haunt Mexico as unrelentingly as one of its beloved soap operas: where is Bermeja, an island off the Yucatan coast that appears to have vanished without trace?
The disappearance of Bermeja is no laughing matter – it would allow Mexico to extend its maritime border some 55 miles further north, helping it to fight off what it sees as American encroachment on its claims to potentially vast oil reserves in the Mexican Gulf.Hunger for news of the missing island has intensified – along with bizarre speculation about what could have happened to it – as Mexico and America ponder a new drilling agreement.
Mexico’s hunt for Bermeja has been given urgency by BP’s announcement last week of a big find in the Gulf, the latest in a series of discoveries that has turned the area into one of the oil world’s most promising exploration regions.
Hmm. What a coincidence.
As for flying the planet, well that might not be so off-the-wall either. See: The science of graviti-ology.
And here you can read about the Nautilus laser.