How dangerous is diplopia (or double vision)?

Affects vision: Severe double vision can be disabling, and thus dangerous, but sometimes people are able to put up with intermittent minor amounts or if found in only certain gaze. Others can compensate for it (i.e. Head tilts). Usually it doesn't directly affect vision such as causing blindness. It's a manifestation of some other eye problem leading to double vision.

Possibly: First newly acquired doubling of vision is very annoying as the world then appears doubled and the true image therefore is not possible to be understood (may have to patch one eye to see comfortably). Secondly you need to identify the cause as that could be from something, particularly in the brain, which might be serious for your health.

Depends on severity: Diplopia can effect your stereo vision or depth perception. This can cause fall and injury. If you operating machinery, driving a car or playing sport it may lead to severe injury to you or others. You need to consult your eye doc for treatment.