If a Kohen marries someone forbidden to him as a Kohen, (1) she becomes a chalalah, (2) their children are chalalim, (3) if she dies he can't go to her funeral (Rashi Emor 21:4), and (4) she can't eat terumah (Sifra Emor parshah 5:7).
What about if he marries a woman forbidden to him not because he's a kohen, but who would equally be forbidden to a Levi or Yisrael? If a Kohen illegally marries the daughter of an Edomi or Egyptian convert (since unlike Amon and Moav, those prohibitions apply equally to men and women, Kiddushin 67a), do any or all of (1-4) apply?
(The same might question have applied in theory to a Kohen who married a woman who received inheritence in Eretz Yisrael in the first generation. I highly doubt any Kohen actually did, especially since there were probably all of about 10 Kohanim at the time. Those are the only two examples I can think of that other than a mamzeret, whose children would obviously be mamzeirim themselves.)