Tina, you're awesome. Thanks for getting back to me so quickly.
Unfortunately, neither point applies to me. I do not have whiteflies. Rather, they are black, very small, and slow. There does not appear to be any sort of infestation -- just some buzzing around. Everytime I think I got them all 3-5 more appear. No larvae, no mites, no dust, no nothing -- just a few buzzing flies.
And regarding the Areca advice, I feel sorry for the other guy, because my baby plant is AWESOME -- she has lived a long life and she's showing no signs of stopping! Sure, she's a little yellow here and there (and she has brown spots and flies), but everyone who sees her is very impressed.
Any advice on the spots or flies would be great. Any if your advice is that I shouldn't care about the spots and flies because my plant is otherwise very healthy, that's OK too. I had just hoped to make those two "blemishes" disappear.