I think Birth of a Nation needs inclusion there. I guess it was inevitable that at some point someone would say "hey, we have these things called plays and we have film, so why don't we film plays?", but the first feature-length film went a step beyond that, writing a work that is first and foremost a screenplay as opposed to something written primarily for the theater. It would take, jeez, a good 30-40 years at least before most movies made this transition. It's also, by the way, racist as fuck - it's literally about how awesome the Klan is - so I do not blame anyone who says "pass".
Citizen Kane is also super-influential in ways that I think make it almost underrated as a film now. I mean, parts of it seem so cliche... but you have to realize, they're cliche in movies because dozens of directors and writers saw what Orson Welles did, thought it was amazing, and copied it into their own work. Also, Star Wars totally kick-started the use of special effects in modern cinema, which in and of itself makes *that* film super influential, but Kane actually used more effects than Star Wars did. Yep. Totally true. Granted, Welles used the effects to make a relatively small budget film look bigger and more bombastic, meaning that the effects themselves are a *lot* more subtle than those of our favorite space opera, but Welles did a crap-ton of really interesting things with the movie. I can't recommend Roger Ebert's commentary on it enough; in fact, I might even go so far as to say that you should watch the movie with the commentary on *first* before you watch it for itself.
There's a similar parallel, I feel, with most of Hitchcock's movies but especially Psycho, North by Northwest, Rear Window, Vertigo, and I guess Rebecca. I've said this in another thread but if you want to get a taste of what Hitchcock might have felt like to contemporary audiences I recommend watching Rope, a movie that for whatever reason was not as popular as his other films (I think maybe because it's static - the whole thing takes place inside of one house and mostly within one room - but I think also it must have been kind of hard to show back in the day). The puzzle-within-a-movie for this is that at the time that Rope was filmed, reels only lasted I believe 6 minutes and so that was the longest any single "take" could be. However, through the use of lots and lots and lots of directorial tricks, from swinging doors to momentarily changing focus from a character to a painting, Hitchcock makes the whole thing look like it was shot in one take. It's also a finely wrought work in its own right, if lending itself a bit to being as much of a stage play as a screenplay, and since it's not as popular it hasn't been copied to death and as such still feels "fresh".
But, like, NxNW practically invented the modern spy film and Psycho the modern psychological horror movie. Okay, sure, you can see Norman Bates coming from a mile away and the Vivien Leigh scene is a bit corny (honestly I kind of love North by Northwest because it's so silly in places - that cropduster scene tho).
Apropos to nothing, but I actually kind of like the movie "Heaven's Gate". Yes, it's best known as the movie that bankrupted United Artists but "flop" does not always mean "terrible movie"... hmm, that sounds like a good topic of its own...