Whilst you are superficially right (there is nothing wrong with the Autocad model) it is the conversion process that is causing your problem. Autocad uses mathematically defined curves to draw circles and similar (i.e. your model) but Shapeways uses polygons in all the formats it accepts (and it takes a lot of polygons to accurately represent a large curve to within a small degree of error.)
When you attempt to convert formats, the software looks at your model, says "This is perfectly nice curves, but I must turn them into polygons, or it won't work." So it does - but it doesn't know how many polygons exactly you want for each curve, or anything like that. Instead it takes a rough guess, and the result is your model gets messed up as shown above.
Two general solutions may or may not apply, depending on what you want.
1) Change the model inside Autocad, either so that it assumes more polygons for each curve when converted, or by converting the curves to polygons yourself.
2) Or, export the model and then manually correct the curves by subdividing and smoothing them using some other software, so as to achieve a decent approximation of the original curves.
Neither of these is particularly handy, but at least one of them should work.