This is a tribute to that classic screwball set-up; the fast talking dame who creates chaos in order to get to know an attractive but naive stranger. So most obviously it borrows from Bringing Up Baby (1938). Only, in What's Up, Doc? Barbra Streisand has a supernatural capacity for causing accidents. Cars crash while she merely passes by.
In Bringing Up Baby, Cary Grant is a palaeoanthropologist with a dinosaur bone, and in this homage, Ryan O'Neal is a musicologist with suitcase of igneous rock... Various other desperate men pursue identical luggage... The film might not have amounted to more than well budgeted fan fiction, except it is full of clever and funny ideas and an obvious deep affection for the genre.
For instance, Streisand knows about a wide range of arcane subjects in great detail (including igneous rock) because we discover she has completed the first term at so many Universities before getting thrown out for causing pandemonium. The stars aren't the equal of the best screwball actors of the thirties, but they are still pretty good.
In the last third, the film steers closer to Looney Tunes than Bringing Up Baby with an extended car chase (including a huge pane of glass carried across a busy road). This isn't as enjoyable as the cute romcom of the earlier scenes. But there is a genuine frisson to be had from the nostalgia for the Hollywood golden age. And the love of the greatest comedies ever made.