If it is a contamination you should see the dots move! Try washing 2 times the dish, at least, and check if there continue to be. It is also possible that they are debris due to mycoplasma contamination. Anyway, if cells look ok, it also is possible that there isn't a contamination but just debris due to cell methabolism!!
The last time I had something like that it turned out to be pseudomonas sp contamination. Under 400x, They appeared as dark sandy materials in the intracellular spaces. You could turn to higher magnification and in my case, I could see rod and spherical structures (depending on the angle) under contrast microscopy. They tend to wobble around a bit. In a couple of days their number overwhelms the spaces. You could confirm it by sending the supernatant for microbial culture and identification.
Decontaminating (with antibiotics) a contaminated culture is most likely going to waste your time. Even if you think you got rid of the infection, the contamination will effect the result of your experiment. And the worst part is after 5-6 weeks they returned to haunt you when you think you had got rid of the contamination.
Bottom line: Consider to start with another set of cell culture.