As you say, it could be dirt on either side of the lens or even the sensor. If so, you could try using a Camera Blower / Brush. I guess I would try the blower and if that failed, send the phone for repair.
Does the number of specks remain the same and do they appear in exactly the same place in the frame?
I'm thinking the issue could either be some dead pixels on camera sensor or even your screen. Are the specs still there when you transfer the pictures to a PC? On your phone, do the specks grow when you zoom in or are they static? If they grow, then it could be the sensor (or dirt), if not then it may be your screen.
If it is dead pixels on the sensor, you should be able to get a warranty repair. If it's on the screen, it's possible there's some threshold under which they won't approve a warrant repair but I think I'd send it off for one anyway.