Eggs: absolutely, throw the white out and eat the yoke
Dairy, I think Mark puts this in the OK category as long as it is the full fat and raw as Dollface said.
The primal law is that if you could find it, kill it, or make it yourself (or at least someone could i.e. I don't live in an area where avocados grow, but I will eat them) then it is fair game. So I think that makes dairy on the questionable end because I would like to see you milk a wild animal.
That said, I love good aged cheese and I consider it to be like a vitamin K2 supplement. I am certainly willing to accept that man has learned a thing or 2 since the paleolithic time and it is OK to indulge in foods that may have not been available to grok, but have a long track record provided they fall into the basic high-fat/protein low-carb box and could be grown in my garden, made in my kitchen, or raised in my pasture (if I had a pasture).
It's grandma, but you can call me sir.