Shulchan Aruch writes that mayim achronim is an "obligation" and some Seforim say it is dangerous to be lax in washing. The reasons given for mayim achronim are that one may have residual "salt of Sodom" on his fingers that could end up in his eyes and cause blindness, to have clean hands for benching, and Kabbala. The first two reasons do not apply today to one who eats with a fork, and therefore many are lenient, although if ones hands are soiled it is definitely an obligation.
Regarding washing the mouth; on the one hand one should also clean his face from any residue of food before benching, but the water from mayim achronim has a ruach ra on it which can be dangerous. Therefore, the Ben Ish Chai writes that one should not wipe his lips with fingers wet from mayim achronim, but Rashi implies that it is permitted and the Kesav Sofer explains that the ruach ra only enters the water when it drips into a receptacle and not while it is on the finger, which also explains why we do not necessarily dry our hands.