Apparently this is common problem with Saturns. The bumper cover, which is one large plastic piece that wraps all the way around to the wheel wells, is held on by three bolts on each side. Quite a bit of it (probably the vast majority of it by weight), hangs out past the front-most bolts, and over time, it begins to sag, causing an unsightly gap at the front:
To fix this, I undid the front bolt on one side (after removing the headlight assembly), inserted a piece of cardboard, and traced around the fender. I then cut out the resulting shape and checked that it would fit under the top lip of the bumper. A local metal shop then cut me two pieces of 1/8" steel in the same shape (for a total cost of $12):
I simply bolted these pieces in place, leaving out the flat washer that was there before, but retaining the lock washer:
Creeeeepy:
That took care of the problem at the sides. The center of the bumper cover is held to the frame by three plastic snap in fasteners, and there's a lot of free play. I replaced these with bolts and washers, tightening them down while lifting the front of the bumper cover:
The last picture also shows some of the weather stripping I installed for gap sealing (to be covered in a separate post in this thread).