Check the pressure

Check the recommended pressure range listed on the gun, and make sure the compressor is putting out a pressure within that range. I've seen similar symptoms when the pressure was too low. Presumably the hammer didn't have enough energy to move the nail, so it skipped over it instead.

Properly load the nails

If the nails are not properly loaded, they may not be fed into the line of the hammer. You'll end up just firing the hammer into the wood, instead of a nail.

Engage the feeder

Make sure the nail feeding mechanism is in place. If it's not, the nails will not be fed into the line of the hammer. This again will lead to you firing the hammer, instead of a nail.

Nail compatibility

Insure that the nails are compatible with the gun. If they're not, the gun may not fire, misfire, or self destruct.

There might only be exposed nail heads at the end(s) of the ridge. The other nail heads should be covered by the adjacent ridge cap shingle, like this (from here):

A professional would hide the last nail heads by gluing an end piece on like this:

That seems like what you are describing. If so, there should be no nail heads exposed.

If you paid for the roof, have the guys come back and fix it at their expense.

As for drip edge, that might vary according to local climate and neighborhood restrictions. (I used to live in a neighborhood which required cedar shake roofs with non-metallic edges. The HOA successfully sued a homeowner who did otherwise.) Check with your neighbors.