Well I hope you are sitting down for this as I can guarantee you, your house has mold in it. With that said there is no need to panic as mold is everywhere.
Now as for whether those black dots are mold, mildew or dust, I can't really tell you.
- Because mold is everywhere and there are so many types, the EPA, CDC & other organizations do not have guidelines or standards on what is considered acceptable, tolerable or even normal.
- The only time it is recommended you test is if you start showing (or they become more pronounced) allergic reactions or flu like symptoms when you are at home.
The best way to clean up small spots like that is by mixing a little household detergent or bleach with water and wiping it away. Once this is done and even before you should control the moisture it needs to live. You control the moisture and it can't grow.
As for testing - do an internet search for a mold testing company. They should be taking atmospheric samples from not only in the house but outside too to get a baseline reading with the samples being sent to an accredited laboratory.
For more information:
Check Sean's building science blog post (here) for an overview.
Read "A technician found mold in my HVAC system's fan blades. How do I keep mold from returning?" a Q&A answered by Mike Holcomb.