When Raj lapses into a fit of anger and kicks his shoes off, he kicks them off in the bedroom (and they land there), but in the next shot (when he walks to the living room), one of his shoes is lying there.
A 747 cannot land in Mykonos airport.
Raj (Shah Rukh Khan) couldn't drive to Athens if an airplane couldn't get to Athens due to bad weather. Also there was no sign of bad weather on their way to Athens.
It is impossible to drive from the island of Mykonos to Athens.
During Raj and Priya's visit to Mykonos, all the sites shown (Lykabetos Hill, Vouliagmeni Cave, St. Constantine Square, Faliro Luna Park etc.) are in or near Athens. Only the windmill dance sequence was in fact filmed in Mykonos.