By Lynn Elber, AP December 3, 2010 A stakeout leads to a smooch on ABC's crime drama "Castle," with Rick Castle and Kate Beckett finally sharing their first kiss. Played by series stars Nathan Fillion and Stana Katic, the pair locked lips in a scene filmed outside a downtown warehouse late Thursday for a January episode. As "Castle" fans know, the show's weekly whodunits share equal weight with the will-they-or-won't-they romance conundrum for the lead characters. Sooner or later, however, TV viewers demand results from such chemistry lessons.