1. Arthur Coleman Winters was President-elect of the United States, not President. Presumably after having won the election, he managed to wrangle the United Nations into designating him as humanity's representative to the Toclafane rather than the sitting President (presumably still George W. Bush) or Prime Minister Saxon.
Except that "The Sound of Drums" took place in either April or June.
Evidence?
Also, the fact that Winters flew on Air Force One indicates that he was, in fact, the President of the United States, not the President-Elect, as only the President flies on Air Force One.
The plane was only identified as Air Force One by the newsreader. It's entirely possible that they reported erroneously. We are, after all, talking about TV news, which is prone to getting things wrong.
And Winters was never referred to in dialogue as the President.
Winters was the President, despite the dialogue.
Surely the character's own description of his title should override other characters' descriptions of his ride's name? And, as I noted before, Winters was never actually referred to as the President.