Subspecialty fellowships use many of the same criteria to choose their fellows as IM residency programs. If you are going straight through from residency to fellowship, you will be applying early to mid 2nd year, and therefore your application will look almost exactly like your residency application. (it's a little hard to buff your CV during your intern year).
Of course, they will pay close attention to your LORs, PD letter (your residency equivalent to the Dean's letter), +/- med school Dean's letter. (I can't remember if I had to send in my med school Dean's letter last year -- I think I might have). USMLE is not really a big deal for most subspecialties. Programs will also look for things that make you stand out -- usually these were done in med school, since again you won't have time as an intern. The more competitive academic programs tend to have a strong focus on research, and research time during fellowship is usually required at these places. So having done some kind of research or having an interest in research is a big deal for the academic programs.
And last -- they are specifically looking for fellows who would be a good "fit" in their program, either by specific research or clinical interests. This is the main difference that I've noticed between residency and fellowship applications. For example, they want fellows who will get along well with the faculty, and who want to pursue similar types of research as what their faculty are good at. Because of this, the interview day tends to be a bit more intense than residency interviews. There are often anywhere from 4-7 interviews in the day with different faculty members, and most of the faculty expect the applicants to have a pretty good idea of what kind of career they want to have (ie academics, clinical practice, etc), as well as have specific areas of the subspecialty that they're interested in.
