I wouldn't say I've mastered any aspects of screenwriting yet, but there are certainly some that I'm a lot closer on than others. Writing short but effective scenes (i.e., the "get in late, leave early" rule), making my descriptions clear and vivid, piecing together an exciting plot -- these are things I'm starting to get the hang of, more or less. But creating interesting and compelling characters who change in a believable way over the course of the script and behave consistently? I think I've got a ways to go on that front.
The genres I've been working in -- action, adventure, thriller -- don't necessarily lend themselves to character work, since the plot is the main attraction and it needs a lot of care and attention. That doesn't mean character isn't important in those genres, though. If I'm going to send you off on an adventure with Main Character X, you need a reason to want X to survive that adventure and get what he wants in the end -- and that reason can't just be "it's a movie and that's what's supposed to happen." The characters give the movie its heart. Without them it's just an exercise -- maybe a thrilling and effective one, but an exercise nonetheless. And that's a lesson I've learned the hard way on script after script.
The mistake I keep making is that I tend to make the inciting incident (the thing that happens early on to kick the main plot into gear) the event that defines the main character; but in a good script, the character needs to already be defined by the time the incident happens. In Die Hard, the writers do a pretty good job of establishing Bruce Willis's character before the Nakatomi Plaza situation hits the fan. He's a cop, he's a likable guy, he cares about his family but he's separated from his wife, and he's disappointed to learn that she seems to view the relationship with less hope than he does. Once we get through all those character beats, his wife is taken hostage; now the marriage is being threatened in a much more frightening way, and he'll have to fight off an entire building full of heavily armed bad guys to save it. This is probably not the way you'd describe the film to someone who'd never seen it. More likely you'd sum it up by saying something like, "It's about this one cop who has to save a bunch of hostages from a building full of terrorists." You might not even mention that his wife is one of them, or that their relationship is strained, or any of those beats I described a few sentences ago. But they're absolutely essential to the movie.
Let's look at it from another angle. Let's say Die Hard has yet to be written and you're trying to write it. You have this idea about an average cop taking on a whole team of terrorists singlehandedly. It sounds great so far -- high concept, big star appeal, potential for lots of great scenes. And then you hit the inevitable stumbling block, namely: Well, why would he do that? Why would one non-super-powered human being try to take down a whole unit of well-trained, well-armed bad guys? ("Because he's awesome!" only works if it's Steven Seagal or Chuck Norris and the movie is going straight to video.) No doubt about it, there better be a pretty good reason in there or the movie's going to seem pretty silly, and not in the fun way that most action movies are silly, but silly in the utterly moronic sense.
So, okay, you deal with the issue by making his wife one of the hostages. Easy. Takes one line of dialogue to establish, and now he has a reason. Is that enough? Maybe. At least it makes the story somewhat believable. Does it make it interesting, though? Not really, because nothing in that one line of dialogue is going to do much to push the story beyond the ordinary. Thus, we have to add a twist. His wife doesn't want him back. Ah, now we're getting somewhere. An ordinary cop takes on a building full of terrorists to rescue the wife who seems to have fallen out of love with him? That's pretty interesting. He's not just trying to save her; he's trying to save the marriage. (By gunning down a bunch of sinister Europeans.) Even if he succeeds, we don't know if she'll take him back.
Clearly, the stuff in the above paragraph is not necessarily what we remember most about Die Hard. But it's essential, because it gives a backbone to everything else in the movie. The pleasure we get from seeing Bruce take down bad guy after bad guy all stems from the fact that we know a little something about his personality and life issues before the action starts going down. We know there's more at stake than just his survival, or the survival of the hostages. There's a marriage that we're hoping gets restored by the end of the film. This doesn't make Die Hard any more than an action movie, but it makes it an effective one.
Side note: People knock Spielberg for always having absentee fathers, divorced parents, etc. in his movies; they take that motif as an indication of his own deep-seeded father issues. I take it as an indication that he understands good storytelling and recognizes that by presenting us with a broken relationship at the start of a film, he gives us something to invest in for the duration.