Are the black dots bothering your cat in anyway? Do they seem scabby or more like skin pigmentation?
The black dots could be freckles which are normal. Orange cats in particular have freckles all over their lips and even inside the mouth. Other ligher colored cats can have freckles, too.
I don't think a trip to the vet is needed. Does your vet have email? If yes, just email the vet the picture and ask if the dots are anything to be worried about.
When I saw your question, the first question in my mind was, "Is this an orange cat?" I see from your picture that he is. Many orange or ginger cats have freckles. I call them 'Hershey spots' because they look like speckles of Hershey's syrup.
Thus, I concur with LTS that those spots are most likely kitty freckles, particularly if they don't bother your kitty in any way. However, if you still have any concerns, or you just want to be safe-- show this GREAT picture to his vet.
But orange="ginger"="redhead"=freckles most of the time!