In most cases, to be more accurate, you would say “I wish somebody took a VIDEO of it.” Very rarely do people use film anymore. They usually recorded it to a SD card. They record to flash memory. In which case, flash memory is not film . Actual action is to make a video. They are not making a film.

A generic verb you can use is record. You could make a recording either by film or video. That implies a moving picture. However, record could also mean voice or photo ( usually not photo. Although you can record an event through photography)

The first two are fine. The third must be, "I wish I had taken a photo [of it]."