1)Apply the technology to the society. For example, in Traveller, ALL interstellar communications takes a very long time to happen, while in-system communications happen at very fast speeds (assuming at least Early Stellar civ). How does that affect politics? News media? Crime investigation? What exactly is it like when your ship breaks 20 hours away from the nearest breathable atmosphere?
2) Take characters out of a vacuum. Give them contacts, families, communities to interact with in the campaign's home system. Mix this with #1, and now how does interstellar travel affect people? Three jumps out and everything you know about your family is AT LEAST 3 weeks out of date. What happens when your grandmother gets sick and no one knows where you are? Between them sending you the letter asking you to come and you arriving, at least 6 weeks have to pass -- certainly long enough for your kid sister to be tried and convicted of poisoning grandma.
3) Don't take Vietnam out, shove it in deep. Traveller is VERY much about Vietnam. It's about people returning from a tour in the military and discovering that they no longer fit in to regular society, no longer really have a home anyway. They have a random assortment of skills which were good for killing people, but aren't really marketable in the real world. In the "ideal" situation, they also have a mortgage on a starship. That's what the game should be about.
3-b) If you don't want to use the Returning Soldier theme, pick some other theme that's from a story about soldiers. Honor on the High Seas, maybe. That wiki link to 36 Dramatic Situations was really good.
4) Play up the differences. Say the PCs travel from a Industrial planet to a High Agriculture planet. Right away, the biggest difference they're going to notice is the FOOD. Three weeks of flavored nutri-soy and chemically flavored food, and the next starport they go to sells farm-fresh onions, still covered in dirt from the field planted just on the other side of the hill from the Starport-E. And as they're biting into that delicious orange, picked right off the tree, have them discover that the planetary data network charges per-minute usage fees, unlike the free network at their last planet.
5) Sci-Fi Stereotypes. The Asteroid Miner's Daughter. The Radio DJ from Fifth Element. The Tentacle Monster Working at McBurgerLand. The Actress From Planet Kansas. Reality TV Show junkies....from space! Create fantastical life situations....and then make them terribly mundane.
The first time the Asteroid Miner's Daughter comes to the PCs seeking help over Mean Old Boss McOverseer, it'll be an adventure! The third time she does it, it'll be a nuisance.