Corey Hart's agency has released video of Hart doing agility drills, and looking pretty healthy doing them. Hart missed the 2013 season with problems with both knees.
Hart is one of the more interesting free agent first basemen out there. Unless the Pirates can get Mike Napoli (which looks unlikely for any number of reasons), Hart looks like the best target for them. His injuries should prevent him from getting too expensive, and he has upside that isn't available elsewhere on the free agent market.
The downside with Hart is that he's right-handed and isn't really a platoon player, so it would no longer be possible for the Pirates to use Gaby Sanchez as the right-handed side of a platoon. By signing Hart, the Pirates can save a bit of money by trading or non-tendering Sanchez, but a lefty free agent like James Loney would fit a bit more naturally into the Pirates' roster. Loney doesn't have much upside, though -- he posted 2.7 WAR in 2013, but that's probably a career peak, given his lack of power and sketchy track record. Also, MLBTR projects Loney will get a two-year, $16MM deal, and I'd hate to see the Pirates commit to two years for a player who was very bad as recently as 2012.