I use presensitized positive resist boards made by Injectorall (Source: DigiKey). You can get very fine traces with experience. I generally stick to wider traces than 4 mil, but I use a "zero width" line as a cutting guide, It generally comes out pretty good and is certainly in the single-digit mil range.
First off, what experience do you have? Are you using positive resist? How are you making your transparencies? How are you etching the developed board?
The etching process is probably one of the most important variables when you go to very fine lines. Some etchants cause significant undercutting compared to others. Considering only the acidic etching baths, I believe ferric chloride has about the least undercutting, cupric chloride is a little worse and is sensitive to the acid concentration, and the peroxide-based etchants (e.g., HCl + hydrogen peroxide) give the most undercutting.
Here are two references related to etch quality:
Printed Circuit Board Fabrication - Etching Outer Layer (Look about halfway down under quality. NB: The equation for etch factor is inverted relative to the reference below.)
**broken link removed** (Shows some typical etch factors.)
In sum, I think 4 mil may be doable by a hobbyist, but it will require some experimentation and very careful control of the conditions.
John
Edit: Here is an image of a portion of a board I made. The smaller traces are 24 mil. The "J " is considerably smaller. As calculated from the font used, the line width is approximately 6 mil. Unfortunately, I had no pictures of the outline I use as a cutting guide, but you can see from the letters, that 6 mill and possibly smaller would be OK.