She is mostly seen with crossed, or otherwise distorted eyes, and may very well have been creator goofing around or making a mistake.
Many people have Derpy as their favorite pony, and there is even a flash game named Derpy Delivery in development.
Derpys real name may be Ditzy Doo, since it is referenced in the Winter Wrap Up episode, and was also mentioned by Lauren Faust.
There's many instances where multiple Derpy's can be seen in a single frame of the show, but the most common ones have only 1, and her eyes are derped out.
There is only 2 currently possible speech lines for Derpy, one being Muffins, and the other being a mess of hushed speaking in a crowd when Trixie, another pony from the show, is showing off.