I'm not saying that personality factors should be taken out of the equation at all. What I'm saying is that they just shouldn't be judged by impressions gleaned during an interview. Part of what would be ideal is some sort of structured interview. I noticed a couple things when I went on interviews: 1) interviewers often asked the same questions and 2) the interviews often tried to cover certain "domains" of questions. I'm guess most try to use some sort if Likert style rating to make evaluations seem like they're not so biased.
Here's an idea that I just thought of. The entire process should be reversed. Applicants should provide information about themselves available to all sites, sites should review said information, then interview applicants based on those criteria. This might in part help to relieve attempts on the part of applicants to tell sites what they think they want to hear. Furthermore, each site could be able to choose questions that it thinks are valuable, or choose response options to questions that are tailored to it's site. We shouldn't have to pay money to send out applications. There should be one core set of questions that are broad in their ability to assess applicants. SITES (not applicants) should then pay to obtain additional information from applicants.
Currently, matching to an internship is more like some sort of crazy video poker or lottery game, whereas it should be more like those online dating sites (okay, that was a pretty bad analogy). Actually, it should be exactly like online dating sites. In round one, both parties create profiles and provide information about themselves and what they are looking for. The first phase of matching is connecting potential matches with each other. Then, additional, standardized site and applicant information gathering would occur prior to rank order list certification. The matching with the rank order lists would continue as it is currently.
Here's an entertaining good example of what the match could be like:
http://blog.okcupid.com/index.php/the-best-questions-for-first-dates/
Instead of flamethrowers (okcupid) we've got the equivalent of rubbing sticks together to create sparks.