Everyone has something in common.
Not in my experience! I've met (and had to work with) people with whom the only thing I seemed to have in common was species and gender.
It doesn't have to be some big hobby or deep love of film. A shared sense of humor, enjoyment of going out, neatness, etc don't sound like resume material but are more than enough to keep two people from boring each other.
Indeed - but they are all things that bring people together
other than sex and plot. If it's a shared sense of humour, what do they both find funny? If they both enjoy going out, where do they like to go?
Getting a sense on the page of what brings people together doesn't mean them having long conversations about the Albigensian Heresy - it can be as simple as a shared reference. Jim Butcher does it in the
Dresden Files - Harry's friendship with the Alphas, beyond kicking monster ass, is heavily influenced by their shared interest in table-top gaming. You don't get scenes where they play, but you do see a game starting, or being interrupted.
I think that a "love interest" can be just a character descriptor - the rarely seen wife that explains elements of the character, like why he doesn't go after the woman flirting with him.
In that case, the "love interest" doesn't really exist as a character - like Columbo's (the 1970s TV detective) wife: he often mentions her, but she never appears. Once the love interest appears on screen/page, what do you do then? I'd say that if s/he is anything more than a walk-on part, s/he needs his/her own character and motivations - as has been said above.
Or, the love interest IS the story - integral to the plot and the main motivator of character development. I really don't think there is a lot of territory between those extremes without writing something that will seem flat.
I think there's plenty of room if both characters are written as real people with their own motivations. If one of them is just a cardboard-cutout "love interest" then you're right: there just isn't enough there to support anything complicated. But if both characters are fully-fleshed out independently, you can run the romance/relationship part however you like - quick or slow, loud or quiet, depending on the prominence you want it to have. It's like any other sub-plot.
Kim Harrison manages to string out a romance for about thirteen books - it's a real slow-burn, loathing-to-love one. It's only one thread among several, and it's never the main thrust of any of the books, as far as I recall, and both characters are fairly central.
Barbara Hambly does it with James Asher and his wife, Lydia: they're both proper characters, but you can also see the relationship between them. The books are dark fantasy/horror - definitely not romance. She also does it with Benjamin January and Rose - they meet, fall in love, and get married during the series, and it's part of the (murder mystery - not cosy!) stories. But even though Ben is the main character, Rose is "real" - and she even gets at least one short story of her own.
Love interests are just like any other relationship between two characters: if they're not forced together by a contract (like being cadets in the same cohort), what do they like about each other enough to spend time together when they don't have to? What do they do when they're not having sex or fighting bad guys? If they end up in a line next to each other in the canteen, or stuck in a lift, what do they talk about?
On the other hand, are you intending it to be something that will last, or just sex for both characters to blow off steam? If it's the latter, it probably doesn't matter whether or not they find each other congenial company - as long as they each find the other physically attractive, they can scratch their itch. Of course, that's another kind of relationship you can show on the page...