To expand a bit...there are also a number of current and former DCTs who post on SDN, they may also have some useful feedback about what they look for in an applicant. Sites all have their own approaches to reviewing and ranking students, but I think there are probably a bunch of shared points across them.
I’m not involved in internship/fellowship training anymore, but here are a few things I would look for when reviewing apps for both settings:
1. Fit. Is this student a good fit for the training program? Can we meet the students needs/wants (in that order)? How would they fit into our hospital/site program? Would our training benefit their training path? Do they need something we don’t offer?
2. How far along in their dissertation are they now? Are they done or on track to finish on time (for post-doc)? Besides fit and big red flags (e.g. disciplinary/academic infractions, DUIs, etc), this was the single biggest factor in inviting a student. My former internship site was one of the few that offered carve-out research time (~4-6hr/wk) that could be used to work on your dissertation or current research, but this is rare. Sites want 100% of their trainees to secure post-docs during the current cycle bc getting stuck in limbo can be rough and sometimes detrimental to a trainee’s career path. It also is something most trainees ask about “where do trainees go for post-doc/fellowship?”
3. Would I want to work with this person? I know this sounds very random, but certain personality styles can be difficult to supervise or even tolerate over the course of a year.