What NP decision problems are not self-reducible?
The paper indeed shows that planar graph four coloring is not self-reducible in the sense of Schnorr. There are several other senses, under some of which every problem in P is self-reducible. See the follow-up paper of Große, Rothe and Wechsung. I am not aware of any other result of this kind. Going over all papers citing the paper you mention (this can be done using Google Scholar, for example), none give any such problems.