Frankly, my feeling is that an intern shouldn’t be judged too highly on their reel. The point of an internship after all is to get better, so a reel that is *too* good out of the box may make the applicant look over-qualified.
I would keep it short and simple, show only your very best in a single reel. Multiple reels with targeted collections are for established guys pitching to specific jobs. Do not take credit for anything not yours, and throw in a small lower-third disclaimer on footage that might be misinterpreted as yours. Don’t show me templated material someone else made that you just dropped a clip onto. These are the same sins as copy-pasting a wikipedia entry word for word and submitting it as your own term paper. Also put the reel up on youtube and/or vimeo, and have a card or something to hand out with the links.
I would be looking primarily at how you compose shots, how you light, is your audio quality good, and can you cut a decent short sequence that works with or without the sound turned up. Bonus if all your levels are consistent and in spec. Bonus if you can show some compositing or Cg design chops, but again, I would not expect an intern to be a master of any of these yet, by definition. Looking for aptitude and potential, not perfection.
The level of competence I want to see just needs to meet a minimum standard that shows you really “get” this, are actively pursuing the craft, and that I don’t have to teach you *everything* from scratch; rather, that you’ve got some basic fundamentals already, and just need further development and experience on more challenging work.