Jackie Chan -- BC as NY
There's a Jackie Chan movie, "Rumble in the Bronx" or something?, set in New York City, but filmed in Vancouver, Canada. It's a bit jarring to have scene set in the middle of the Bronx, but when a shot looks down a street, there just past the city limits are tall, glaciated mountains! It wasn't just an occaisional small, quick goof, they really made no attempt whatsoever to hide the looming mountains.
Of course that wasn't a documentary, but most of the time in situations like that they at least try to avoid gratuitously "that ain't New York!" shots.