You can search on or around nearly anything. That's one of their selling points to customers. The search function is multi-faceted, in that 1) it can index the data of any files you upload to Palantir (making everything text searchable), 2) Analysts can indicate specific attributes of an entity just by highlighting text in a file and marking it as a DOB or SSN or whatever. 3) The # of attributes is nearly limitless.

One of the primary screens in Palantir is a simple search page designed to work (and look) like Google, to search upon your entire database however you'd like. You can enhance the search function via the various attributes built into your installation or using advanced search tools. So I guess a "fishing expedition" in the traditional sense is very easy, as it's limited by the data you have, not the system itself.