This grammar error only makes itself obvious in the written word, but it does seem to be fairly common.
Use anyone if you can substitute it with anybody.
- Did anyone else hear Andrea Mitchell use the slang (read inappropriate) word “diss” this morning during an MSNBC report? (You could say Did anybody else hear…?)
- Did anyone care? (Did anybody care?)
As far as using any one, it means any single one. Try this: If you can substitute any two, then use any one.
- Did any one of the anchors find it odd to hear a reporter use diss? (You could easily say Did any two of the anchors find it odd?)
The same is true for everyone; it can be substituted with everybody.
Everyone is here. (Everybody is here.)
Every one means every single one.
Every one of the guests is here. (Every single one of the guests is here.)