Dilbert and Dogbert don't have mouths in the comic strip, but the animators needed to give them mouths for their dialog. They compromised by giving them mouths only when they spoke. Since the show went off the air, a mouth has been drawn on Dilbert in the comics, usually to show either surprise, screaming, or anger. (Dogbert, however, continues to be drawn mouth-less.)
The name of Dilbert's company, Path-E-Tech Management, comes from the merger of two companies in the first season: Pathway Electronics and E-Tech Management. It is also a play on the word "pathetic."
'Kathy Griffin' was appearing in Suddenly Susan (1996) when this show aired, and her NBC contract at the time did not allow her to receive on-screen credit for the voice of Alice. She's mentioned by name in DVD extras for The Complete Series, and interviewed about it, but her name is not in the credits of any episode.
Main theme, composed by Danny Elfman, was taken from the theme for the movie Forbidden Zone (1980) (the first movie for which Elfman composed music) - hence its title, "The Dilbert Zone".
The characters of Wally and Alice are based on a couple of Scott Adams real-life former coworkers. Wally comes from a man who wanted to take a generous buyout package from the company Adams worked for - but one for the worst performers. This gave him an incentive to be totally lazy, incompetent and surly. Alice's inspiration was a woman who made two grown men cry.