October 3rd in "Mean Girls". Rex Manning Day in "Empire Records". May the Fourth in "Star Wars," kind of (remember that part in the Star Wars re-release when Wedge looks straight to camera and says "May fourth is my favorite day, Luke Skywalker ol pal"?)
Just have a character mention a specific date and your movie is guaranteed to trend on Twitter every year on that date because we're all extremely bored on here. Then people will tweet about NOT CARING about the day, but that'll only be more publicity, and long story short, you will have made the greatest film of all time (internet-wise).
Throw in a bunch of scenes where a character makes a really wacky face and holds it for a few seconds, and position the camera so there's a ton of extra space above and below the face for the easy addition of Impact-font meme text.
The context of the scene doesn't matter, either. "Bashful Liam Neeson"? "Winking Christina Hendricks?" "Coquettish Ian McKellen?" Doesn't matter, just make it lightly wacky and let people run it into the ground.
Boom. Hit meme = immortal movie.
Just throw a bunch of fun, subtle, referencey-stuff in the background -- DVDs of the director's other movies, Stan Lee / Stephen King cameo, name a hospital after one of the director's idols, etc -- and your movie will live on forever in the form of "17 Things You Might've Missed in the Movie [Whatever]" internet lists.
Mind = BLOWN. Is a thing people will say, about the Easter eggs. Good filmmaking!
Pack your movie with dozens of shots of one character saying a snappy, quotable quip that could apply to a broad spectrum of situations in the hopes that some of them get turned into memes that commenters can use to belittle (or praise!) things on the internet or each other. Or let them make up their own stuff, like Snape saying "DAYUMN GIRL" or whatever (doesn't matter if Snape isn't in your movie, just throw him in there).
And to ease the GIF-ing process, just have every line in the movie appear as floating yellow italicized text as the person says it. Hell yeah, man, now you're the GIFING TREE over here.
Just play the odds -- if you have literally hundreds of children in your movie for some reason, almost certainly one of those kids is gonna go on to become super famous. Now, every few weeks on the internet, someone's gonna post a screenshot of your movie with a super-young version of that actor and be like "OMG check out Young Starro Guy!!! He was the boot shiner in the background in the 'Boot Shiners Convention' scene in this old movie!"
Now no matter how dumb your movie is, it's a cocktail party anecdote. (For a very very boring cocktail party, but nonetheless.)