How did Cole end up in WWI, if he was in the U.S.?

There's definitely a component that lets you alter not only the time, but also the place you're being sent to. We don't see anything in the movie that makes us assume that the machine can only take its travellers to one place, do we?

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I didn't like the Godfather, so what?

"Basically it's a time machine, not an intercontinental traveling machine. Each time he goes back in time, it's always the same place, but this one time, he is in Europe, all of a sudden. Why?"

It was hinted that other time travellers before Cole were accidentally transported to other countries. (Like the doomsday prophet in 14th century England.) After returning from 1990, the voice in Cole's head said "You're lucky you didn't end up in ancient Egypt." This can be put down to the teething problems the scientists were having with the technology, the trickiness of getting the co-ordinates right, etc.

When dealing with time travel in SF stories, another issue that is often brought up is spatial displacement. While a person is time travelling the earth is also moving, so it's reasonable the time traveller would end up in a different place, with some potentially nasty consequences.