Is double vision a side-effect of a neurological problem?

Depends. Usually double vision is divided into monocular or binocular (eye alignment), and then eye alignment can be affect by the muscle (weakness or overaction) or mechanical issues affecting muscles (orbit) vs. Neurological input to the muscles, or a brain problem.
Can be. Eye motion is a complex activity coordinated by 12 muscles. This orchestrated by the brain hence, a neurological problem can indeed cause double vision. Sometimes however, the problem is structural say in the orbit which causes double vision. Best to be checked out thoroughly and quickly by an ophthalmologist.