My understanding might be a little off, but I feel like we're having two separate discussions here: one on perspective and one on distortion. Distortion comes from the lens, and there's nothing you can do to change that before you take the shot. Perspective comes from where you're standing.
In BackDoorHippie's great example, the weird "carnival mirror" look to the girls face in the 16mm photo isn't coming from distortion in the lens; it's coming from the fact that the photographer has to stand inches away from the subject to fill the frame with her head at 16mm. The perspective is much closer than we would normally stand to someone, so it looks odd. Take a look at the far left 16mm photo (the head and shoulder shot). It looks much more normal, since the subject is now further away. The perspective is more natural.
I don't do a lot of portraits, but it's my understanding that the 105mm is a popular portrait lens because it lets you get a closer shot while still maintaining a normal distance from the subject, resulting a photo with a natural looking perspective.
I also think about it this way: Put identical 35mm lenses on an FX camera and a DX camera and take a photo with each where the subject fills exactly the same amount of the frame. The perspective will be different, since you'll have to stand farther away with the DX camera to get the subject to be the same size in the viewfinder. In that way, the 35mm on the DX will behave like a 50mm (52mm and some change I think if you're being exact) when it comes to angle of view. Distortion in both will be similar (not identical, since you'll lose some of the edges on DX). I've always found it pretty hard to pick out distortion though, unless it's really severe or the photo involves straight lines or perfect geometric shapes.
Hope this helps! Feel free to tighten me up if my concepts are off.