Wikipedia says that Andaz was the only movie in which Dilip & Raj appeared together.
Other note: Nargis is sometimes said (at least recent statements) to have worked mostly with Raj, but I find that she worked almost as much with Dilip (including times I was not sure that they formed a jodi).
Though there may have been some times where the plot & script was shaky and nearly confusing, I believe there was more to this film than what met the eye. Here are my thoughts:
This could have easily turned into a "guy rescues girl from life-threatening accident and they fall in love, despite her having a fiance who returns in the middle of the film to much angst." It wasn't that. Instead, it got into an issue that comes up a lot, especially in the present day: the issue of the so-called "friend zone." It's hard to not look at this film with 21st century eyes, but I'll try.
First of all, I've been in many situations where a guy has taken to me, but I consider him just a friend. And when I have to tell him that we don't see eye to eye, it really sucks. I really felt for Neena (Nargis) in this film. In the scene where she tells Dilip (Dilip Kumar) to go away forever, I could feel her pain acutely. Sometimes it takes a lot of vehemence and force to convince someone that their feelings are not mutual. And nearly always, especially regarding a close friend of yours, it often is just as painful for you as it is for them. You never want to hurt a good friend, but you know by telling them that you don't feel the same, you will hurt them in some degree, no matter what.
There is also a broader metaphor here about the war between old ideals and modern sensibilities. Like other films of the time, the old ideals are distinctly Indian, while the modern sensibilities have an air of British colonialism, remnants of that regime sticking around a few years after independence. Neena's father and the old, ridiculous guru serve as voice boxes for those old ideals, whereas the audacity of Dilip flirting and dancing with an engaged woman (granted, he didn't know it at the time) shows a modern lack of respect for those old ideals. Rajan (Raj Kapoor) and Neena also have an old-ideal relationship; though not on the surface, it is felt at its core, when she says she worships him like a god, offering him flowers. That goes back to the whole "husband is God" thing that has been with humans for centuries and still exists in some relationships today.
Now, for the performances. The leading trio did an excellent job, but did I expect less from three of India's greatest actors of all time? Dilip did best; his lovesickness transmuted into a frenzied fury nearing the end was a great role for the "Tragedy King." Add the fact that he was looking quite good in 1949, like a Marlon Brando of Bollywood! I'm not a big fan of Nargis playing the spoiled, frivolous rich girl, so many of the first half scenes are throwaways for me, but toward the end she has a couple of good Mother India-like intense stares right into the camera, and that deep well of turbulent emotion in her eyes lends her a shine. Raj was good for film purposes; the comic relief, per usual, but there is an unappealing pompousness to his character that he plays well. Watching him and Nargis interact coolly with their curly-headed baby in tow later in the film reminded me of scenes from Gone With the Wind - they would have made a good Rhett and Scarlett.
The music by Naushad (of Mother India fame) was good, if not catchy. I may need another few listens to the soundtrack to catch on. The script and plot was the weak link of the story. The opening hour and a half felt quite empty, with all the action packed into the last, say, 30 minutes or so. I feel it would have been a stronger film if the action would have been parceled out more evenly throughout the film. What came to a shocking denouement came disappointingly out of nowhere and didn't last long enough for the emotional effect the filmmakers probably intended. Don't get me wrong, the young handsome trio were nice to look at, and it was interesting to follow their angsty love triangle, but I feel like I would have gotten more attached had they spent less time on fluff and more time on substance.
Nevertheless, a good film that moves quickly and certainly isn't boring. I was looking forward to watching this one and wasn't overall disappointed. The pleasure of seeing three genius actors, plus a genius director, at work is well worth the watch.