I just rewatched "Falling Down" last weekend
It's a personal favorite. Your review is mostly spot-on. But I disagree with the darkly humorous content running out after the gunning down of the (admittedly funny, and OTT) Neo-Nazi Frederick Forrest character. What about the old man having a heart attack on the golf course? "Now your gonna die. Wearing that stupid hat. How's it feel?" LMFAO!!! Gets my goat every time.
For a dark comedy, the movie still attempts to have a serious, social commentary tone. The film doesn't really know if it wants to be serious or funny. That's the only problem I have with it.
Critics gave it pretty mixed reviews, but Roger Ebert liked it (three stars out of four).