What do principal investigators (PIs) look for in prospective post docs?
Postdocs have an absolutely critical and unique role in a research group.  They have more research potential than anyone else in academia, because they are both full time on research and yet experienced, not students.  They are also very expensive and a rare luxury that comes only with heavy investment from a funder or university.

The first thing I look for therefore is demonstrated proof that the candidate will take good advantage of the expensive opportunity they are being offered.  Forms of evidence:  


existing publications
publications in prep.
letters of reference


These should show that the candidate has skills in what needs to be done, and the determination and internal motivation to be a successful academic.

The next thing I look for is evidence that the candidate is very likely to employ those skills in the area that I am funded for them to research.  This is done through open and frank conversations with the candidate about their research and career goals, what I need, what they need, where they intend to go next, etc.  A postdoc is at a critical time in their career, and everyone should know that they need to produce papers out of their PhD and that they may leave early if the right lifetime opportunity comes along.  I try to negotiate in advance about what research I absolutely need them to complete, what further I'd like them to complete, and to discuss writing and research schedules such that they can meet both of our needs and wants, preferably through some synergy (e.g. of the possible outcomes of this project, which would best suit both of our goals?)  I then try to agree a schedule about what research will be done when, what is the earliest date they'll start looking for their next position, when will they or we start writing the next grant or fellowship bid etc.

These negotiations give me not only a sense of how much I can expect us to accomplish if I make this hire, but also how well we can work together and how similarly we understand our responsibilities as academics.

Finally of course there is a luck element:  if there is more than one viable candidate, the one who seems likely to be the best fit wins.