Have new roof with exposed nail heads at ridge. Roofer's fix was to cut tiny squares of shingle and goop/glue to top of nail heads. Need inputs from roofers; what is the proper way to fix the exposed nail heads? Any code number for this? Also, have they stopped using drip edge?
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):
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.