I have never seen Stargate, but I'm guessing Daniel Jackson had the added incentive of immersion, as well as the advantage of being fictional. ;) If you want a good portrait of how linguists work with actual language, I'd look at Milo Thatch from Disney's Atlantis: The Lost Empire. They're pretty unrealistic about a lot of things, but the way Milo communicates with the Atlanteans and studies the language is a bit more like it--halting but enthusiastic.

I do pick up a lot of things from immersion, though--I can tell you a lot more about the difference between Kenyan and Tanzanian Swahili after I visited those countries, or a few interesting aspects of Spanish that it'd be hard to explain in a textbook. That's the best way to learn the subtexts.