It had already been established that Luke’s an amateur mechanic – and that that droids are fairly common household appliances. We can only guage the damage by Luke’s reaction, and he doesn’t even give us an “Oh man, Uncle Owen’s gonna be pissed!” So when the next scene glosses over the repair like it’s no big deal, the audience takes the movie’s word for it: this skill is no big deal. (Of course, if your droid has been blasted completely into pieces, that would take some tougher skill checks or the help of NPCs.)
Now, this is partly because Star Wars has already shown us a world where hyperadvanced technology is pretty commonplace – no more unusual than cars and appliances in our world. It’s exciting that Luke gets to grow up and fly a spaceship, but it's no more exciting than for a modern teenager to grow up and fly an F-16.
But it’s also because of The Way Skills Work In Stories.
The Way Skills Work In Stories is largely a matter of what the story needs at the moment. In this case, the story needs to move on past a minor problem to more important things. Luke’s a mechanic, so he just uses his mechanic-ness on the detached arm. Easy. If the movie was about the complexity of droids, or about Luke-the-genius-mechanic, it might devote more time to this scene. But it’s not. (This, actually, is one of the many ridiculous things about Phantom Menace: it tries to get us to see Anakin as a genius based on the fact that he’s built a droid – in a world where droids are as commonplace as vacuum cleaners. /rant)
Even plot points that are far more important are handled this way in the movies. In the Ocean’s films, everyone routinely passes Intelligence and Contacts rolls that ought to be enormously difficult in the real world.
I guess what I’m saying is, people (usually) play RPGs to experience an adventure that’s like the movies. So shouldn’t skill checks work the way they do in the movies?
As a GM, I’ve spent lots of time worrying about DC because I’m trying to make it “realistic.” I don’t want to make it too easy. But skill difficulty should be based on genre, not realism. Whatever skills these characters use every day (and if it’s a high fantasy setting, that might mean casting certain spells – if it’s an “elite thieves” campaign, that might mean lockpicking or picking up intel) you can really keep it simple: any normal lock is easy for these PCs to pick, and only extraordinary locks are hard. In other words, the lock on a tavern pantry can be about the same as the one on a wealthy merchant’s front door, since neither one is going to have anything plot-shattering behind it. Now, the one on the bank vault or the crime boss’s door, that one should be tough.
One more point: when your players are picking a lock, remember that it’s really all about story, not the lock. If they get it open, then fine – simple as easy as reattaching a droid arm, you might say – and adventure awaits on the other side. If they don’t get it open, then *gasp* this must be some kind of Extraordinary Super Lock that’ll require a different tool, a tip, or even a side adventure to get it open. …And of course if they fail on an easy lock, you can just quietly change it to an extraordinary lock, as if it had been that way all along. Why would there be such a diabolical lock on this seemingly normal cabin? What secrets does this humble facade conceal? Questions like that make it as much an adventure for you as the players.
Bonus Fun: while searching for pictures of Luke repairing C3PO, I found this picture. I guess the real skill check in this scene was being able to breathe in there.
Bonus Fun: this truly incredible piece of literary criticism that will blow your mind and make you question everything you ever believed about Star Wars or about yourself as a person.