ST:TNG:13 - "The Big Goodbye" (Stardate: 41997.7) - this is the 13th episode to go into production but the 12th one aired on TV. It's also the first episode to really go in depth into what the holodeck can do (although seen in two episodes before this including the pilot episode "Encounter At Farpoint) - in this case, you see Picard playing what will become his favorite character, that of 1940s detective Dixon Hill in many episodes (and this character will have a welcome cameo in the feature film Star Trek: First Contact). Also, the part at the beginning where Troi teaches Picard the exact greeting at beginning of film to say to an alien species, is just like in the feature film Star Trek: Insurrection (also at the beginning when Picard is coached by Troi when he is about to meet the new alien delegates). Oh and watch out for Dr. Crusher swallowing gum!
Review of The Big Goodbye
