A possible solution to some of the problems would be creating (and for official videos, requiring) a chain of trust, enforced by strong crypto, starting at the original recording device and ending at the viewer's display. Some trusted parties would also probably have to vouch for the start of the chain, too.
That basically sounds like the dream world of DRM people, though.
How could it tell coordinates in either space or time? non-military-grade GPS is spoofable (not really easy yet, but easier by the day) and GPS signal is rarely available inside a building (and sometimes just under an awning or cloudy days, or near skyscrapers - GPS in NYC is horrible; mobile phone GPS are as reliable as they are because they take cell towers and wifi into account).
The important point is " making it harder " - but how hard is hard enough depends on the party in question, and for many important ones, the simple answer is "not hard enough".
That basically sounds like the dream world of DRM people, though.