It's no secret that modern technology has really limited the types of stories screenwriters can tell. Romeo and Juliet's plot would totally fall apart if it was set in a world where people have cell phones. The idea of going Around the World in 80 Days isn't very exciting now that we have planes that can go faster than the speed of sound. Now that science has proven that radiation poisoning is irreversibly fatal that scene in Stark Trek Into Darkness where Kirk's body is bombarded with a lethal dose of nuclear juice and then he is immediately resurrected by magic alien blood looks pretty silly.
Also: Ball of Fire would make no sense in a world where the internet exists. It's a screwball comedy from the early 1940s about a nightclub singer named Sugarpuss O'Shea who has to go into hiding after her boyfriend is arrested and charged with murder. At first it looks like she's going to have to bide her time in a rat infested warehouse, but she happens to meet a nice bookish fellow named Bertram in the nick of time. Bertram is an encyclopedia writer who is struggling to write the definitive article about slang because he's so out of touch, and the two of them strike a deal: he will make one of his seven assistants hand over their bed to her for a few nights if she'll teach him all the hep words the kids are using these days.
Now there are two obvious ways that this story doesn't work in a modern setting. The first is that Wikipedia has eliminated the need for professional encyclopedia writers, which means that Bertram wouldn't have a job, thus he would have no reason to make friends with Sugarpuss. The second is that Urban Dictionary has allowed even the squarest of people to easily research any slang word they're curious about, so even if Bertram wanted to write about slang he wouldn't need help from Sugarpuss. The firehose of information that we call the internet has completely destroyed these people's meet-cute: the 2015 version of this story would see a completely unemployable Bertram moping around his mom's basement while unbeknownst to him the girl of his dreams was stuck bunking up with some angry rodents across town. That scenario is... a little less romantic.
Of course, Ball of Fire isn't trying to be timeless - it's a stylized update of the Snow White story that was meant to bring the story up to date to the 1940s. Taken on that level, the movie is a lot of fun, particularly because the movie's up-to-the-minute vernacular is pretty quaint now. Bertram is dumbfounded when Sugarpuss describes her type of music as "boogie-woogie" and he is bewildered when she explains that a "yum-yum" is a kiss shortly before she kisses him. Today no one would use any of Sugarpuss's lingo in everyday conversation - the only context I imagine you would hear someone use words like "skiddoo" or "skeedaddle" now is a Saturday Night Live skit that was riffing on an old movie like this - but that doesn't mean that this movie isn't aware that these slang words are pretty ridiculous. In fact, that's the whole joke of the movie, because most of it's jokes are based on its wordplay.
Actually, the film is dated in the same way a Shakespearean play is dated. Yes, our language has evolved enough that some of these puns no longer work, bu it's obvious from the pace of the patter that a joke is taking place, and if you can put yourself in the story's headspace then you'll still have fun even if you don't get all of the puns. You can take this point even farther and argue that the whole enterprise is Shakespearean, because he liked to take well known tales and put his own stamp on them, and this film definitely puts it's own stamp on the Snow White story by swapping the gender of the leads. The fact that it's Bertram who is meek and living in the proverbial woods with the seven dwarves pushes the story in an interesting direction, because it means that Sugarpuss is slotted as the tough one for most of the movie (which makes sense given that she is a gangster's moll while Bertram is just a bookworm). Of course, this is a movie from the 40s so at the end of the day Bertram is going to have to fight her beau for her hand (after all he is a man) - but until that ending it's an interesting dynamic.
Ball of Fire is a little old fashioned, but it's the sort of old fashioned that reads as classic, not corny. (Corny, by the way, is another word Bertram has to have explained to him.) Yes, Wikipedia has destroyed the basic premise of this movie - but that's fine. After all, Ball of Fire is itself just an update of an even older story, so you would expect that any theoretical remake of it would also have to be an update. But good luck to the screenwriter who has to figure out how the man who lives with dwarves is gonna meet the woman who lives with rats even though they have nothing to give each other and no interests in common and no public space to meet in - I can imagine that's going to be a bit of a hurdle to overcome.