That looks like dust on the DLP chip. It's a fairly complex piece of work to take the projector apart all the way down to the DLP chip to carefully clean it. There are videos of doing this at www.youtube.com/fixitfrank on some various models.

This is a fairly common issue with DLP projectors unfortunately, and in a clean room it doesn't happen as often, but does occur.

I've seen someone who just did this in his home. You typically will not make it worse by doing it yourself. It's not like a ton of dust will instantly resettle on the DLP chip if you do it in your home. You just want to be super cautious when doing the cleaning work. It will typically drastically improve the chip if you do a cleaning once it is this dirty. I have a HT2050a that I need to do a cleaning of because it is really bad. I will just do it in my dining room one weekend.

I'm not aware of many electronics repair shops these days. It's just not that common anymore. Certainly you can send it in to NEC and they will do it, but that's not worth it at all.