Die Hard exists in a land of nostalgia and fan reverence for most fans of action films, which can make it hard to look at objectively. The value of this video, where Bob Chipman spends an epic 30 minutes talking about all the things the movie gets right, is that it allows us to remove the film from its cage behind our rose-colored glasses and place it back in the cultural subtext from whence it came.
Chipman's insights are worth listening to if you want to understand why the film has stood the test of time as a great film, not just a film with which we grew up. It's a tense, relatively small-scale story shot and scored like an action film with a much larger scope. The characters are all expertly designed and executed by both the writers and the actors, and the way information is shared with the viewer but not with the other characters allows you to feel like you're on the inside in a way that sets you above the other characters.
This is all interesting stuff and will help you understand Die Hard on a few different levels, but the real fun is realizing just how odd the casting of Bruce Willis seemed at the time. He's an obvious action star today, but his starring turn in Die Hard was a huge risk that made little sense. It paid off, but you have to remember that the job he left was that of a pitch man for wine coolers.
Give this a watch, you're going to have a good time.