Okay, so "Wings of Desire" was beautiful... but WHAT even was that?

So, I just finished watching "Wings of Desire" and WOW, visually STUNNING. Like, Berlin looked absolutely gorgeous, especially in the black and white parts. The whole angel thing was pretty cool too, just floating around eavesdropping on everyone's thoughts. But I'm kinda lost? Like, I get that Damiel fell in love with the trapeze artist, Marion, and that's why he wanted to become human. The whole wanting to experience everything thing was relatable, I guess. But the random appearances of Peter Falk? What was THAT about? Was he an angel who'd already made the switch? And the black and white turning to color thing was neat, but did it MEAN anything beyond 'he's human now'? I think I liked it? But I also feel like I missed a bunch of stuff. Did anyone else feel kinda confused but also strangely moved by it? Maybe I'm just too used to movies where everything is spelled out for you, haha. Seriously though, if anyone has some insights, please share! I wanna know if I'm just being dense or if this movie is intentionally super artsy and ambiguous.