Based on my experience working with startups, here are some key skills that most founders/managers look for in new college grads for startup positions:
1) Strong Analytical & Problem-solving Skills: Many problems tackled by a startup tend to be new product problems or technical challenges that have not been solved before. Thus, a sharp mind that can creatively explore solutions tends to be more important than a person's current knowledge.
2) Strong grasp of fundamentals. A sound understanding of basic concepts shows that a) the candidate learned and retained knowledge well in the past, and b) the team can build on top of a common language and shared foundation when tackling new problems with the person.
3) Intellectual curiosity: It's inevitable that most of what a recent graduate needs to know will be learned on the job; therefore, how dedicated and fast the candidate is at learning is usually more important than how much the candidate currently knows. Typically, one can assess this quality by seeing how much the recent graduate learned at his previous internships and jobs. Someone who's worked at a place like Google for six or more months but who hasn't taken advantage of Google's codelabs to learn about core engineering abstractions designed by some of the company's best engineers, or delved into design docs of some of their major systems raises a potential red flag.
4) Effective communication and the ability to clearly convey ideas. IBeing able to convey ideas effectively usually correlates with a person's ability to think in terms of the bigger picture. Those who get caught up in too many specific details have a harder time explaining things, and miscommunication or the inability to share ideas in a startup can drastically slow down execution speed.