Hi Maury,
Not sure why you're getting that output. An arc will normally produce smooth corners not facetted ones (except for where it joins onto the straight edges) You'll normally only get all the vertical edges showing if you have exploded the curve before extruding the face.
Anyhow, to solve the problem, just paint over all the vertical lines with Eraser whilst holding Ctrl down. Done!
[Command on Mac OS]