The cast, obviously, is great, and each of them is given a little space to enjoy their roles. Wu-Tang member RZA is particularly funny as a self-serious "WU-PS" delivery driver. But the problem with a movie with so many cast members as slowly-paced as this one is that none of those great characters really get that much to do. They all have a few scenes to themselves, but Driver and Murray shoulder most of the load. Steve Buscemi wears a "Keep America White Again" hat so you know what you can expect whenever he's onscreen. Tom Waits pretty much spends the entire time in the woods, muttering about mushrooms and "toxic lunar vibrations." Chloë Sevingy plays the only female cop -- coincidentally the only cop to immediately lose her cool in the face of violence.
There are a lot of funny moments and little visual jokes as well (the large Adam Driver in a teeny SmartCar), but most of the humor is situational -- as in, it's funny to hear these actors say lines like "toxic lunar vibrations" or "ghouls," but the script itself, after a while, loses a lot of its charm. It also doesn't help that, for some reason, Jarmusch picked a monotone, Yorgos Lanthimos-esque style of delivery for all of his actors, having them speak all their lines as if they worked at the DMV. There's no clear reason for doing it like this, other than that maybe Jarmusch thinks all small-town folks are slow talkers.
The film takes a dive as soon as the inevitable metaphorical nature of the zombie apocalypse is revealed: the zombies, when they're not thirsting for the meat of humans, gravitate towards things they loved in life, murmuring "cooooffeeeeee," "wiiiiiifiiiiiiii," "xaaaaanaaaaax"... it's not hard to unpack. By the end, you can't help feeling like you've seen this movie done before, and better, with much more life in it than in Jarmusch's sodden experiment.