The very first line sets the scene, although the specifics aren't important. The fact that this is the Hollywood Hawaiian Hotel is not important so much as is the fact that this is a place, and the singer is there, although the alliteration is nice. The next line is crucial, however. Looking into an empty glass is a very profound piece of symbolism. Recall the old metaphor about some glass or another being half empty for a pessimist or half full for an optimist, but here, the glass is all the way empty, and optimists are simply shit out of luck. Moreover, the singer is staring into this glass, which is to say, he's dwelling on the problem.
And now, here come the Gypsies, fabled as fortune tellers. Given that the singer's situation is dreary to say the least, and since the Gypsy wasn't lying, then the device of the person of the seer--later also referred to as 'mystic'--must have fortold such a calamity, or so he thinks. The next two lines are straight forward enough: it's Miller time.
Going back to the setting for a moment, since the Hollywood Hawaiian Hotel is just a place, and being in such a place only describes existence, then the sinking of California where the Hollywood Hawaiian Hotel is located is the end of that place, the end of existence. The singer is alluding to the end of the world, to Hell or highwater as augured by "the mystics and statistics". Once it comes, he's still not free from his responsibilities; he can't die until he's atoned for his sins. His bill is an enumeration of regrets and mistakes from which he cannot escape.
The next stanza is poetic wailing. Don't the sun look angry through the trees? God (the sun) must be really pissed! Don't the trees look like crucified thieves? Even the trees are angry and accusing (also an allusion to Christ; Zevon himself remarks in the liner notes to the anthology I'll Sleep When I'm Dead that a friend of his thought the trees were the men crucified alongside Christ). Don't you feel like Desparados under the Eaves? Desparados are bad guys. Don't you feel bad just sitting here? Isn't it awful; I should be out doing something! But: Heaven help the one who leaves. It's safe here; it's dangerous out there. "He who does not strive with others will be free from blame." You could get hurt out there, among the trees, under the angry sun.
The whole next stanza finally defines the poor man's entire predicament. Physical malady in line fourteen; spiritual and emotional problems in line fifteen; a very profound statement aobut modern culture, about being a slave to the world without succor except for sleep in line seventeen; and finally, a repetition of the paranoia one gets when stuck on hard times: that perhaps the world is out to get them. This time, in line eightteen, the statement is much, much more personal. The sun (remember, that's God) doesn't just look angry in general, it looks angry specifically at the singer.
At last, the song comes full circle and revisits the setting. He's still in the Hotel, only now, he's not concentrating on the glass. Now, he's listening to the air conditioner hum, to some outside advice, as it were. In the singing of the song, the humming goes on for about three stanzas worth of Warren Zevon vibrating away. Then it breaks into lyrics:
Look away down
Bower avenue,
Look away-ay down.
These lyrics are sung in the same beat and rhythm as the humming had been hummed, suggesting that this is the air conditioner's advice, a pattern in the chaos, if you will, giving out directions. All that this means is, "Get out! Get off your ass and do something, the sun and the trees and Heaven be damned!"
All in all, it's a story about human problems and the human ability to deal with them. It's the cycle of depression. It's fantastic artistry.