What are Soapy's crimes?

He has a good dinner at a fancy restaurant and doesn't pay for it. We get the impression that Soapy's done this before as he seems to know exactly how the scam works. (Or should work, at any rate). The idea is that, when he doesn't pay for the meal, the waiters will call for the police, he'll be arrested, go before a judge, and then—voila!—he'll be sent to a nice warm prison cell for the winter. But the head waiter takes one look at Soapy's shabby clothes and shoes and turns him out the door before he's had a chance to sit down;
Soapy throw a big stone through a shop window. Surely, a cop must arrest him now! But when an officer of the law turns up, he flat-out refuses to believe that Soapy could've broken the window. After all, criminals who break windows tend to run off straight away; what they don't do is hang around and wait for the cops to arrive;
Soapy tries to pull the restaurant scam again. This time, he's able to get his foot in the door and has himself a slap-up meal. But even after Soapy tells the waiters he doesn't have any money, they still don't call the cops; they simply throw him out into the street;
Then Soapy tries a different tack. He approaches a young woman browsing at a shop window display. The plan is that she'll get spooked by what she thinks is a weirdo and complain to the beat cop standing nearby. But instead of running off, the woman‚ much to Soapy's exasperation, takes his arm and smiles. It's not spelled out explicitly, but the suggestion is that the woman is a prostitute who's glad to have found another customer;
Soapy's getting increasingly desperate now, but with the winter coming on, he can't give up his quest for a warm place to sleep just yet. So outside a theater he starts shouting and hollering, pretending to be drunk. But the cops still won't lay a glove of him. They ignore him, thinking he's just a harmless college kid in high spirits;
Finally, Soapy steals a man's umbrella. But we get the impression that the man stole it himself and so naturally doesn't want to get the police involved. So he walks off, leaving Soapy angry and dejected. His plan seems to have failed, miserably.

Soapy commits (or tries to commit) several non-violent crimes in his attempt to be sent to jail on Blackwell's Island for the winter. First, he tries to eat a meal at an expensive restaurant (though he cannot pay for it), but he is thrown out by the waitstaff. Then, he throws a brick through the window of a shop on 6th Avenue, but a cop does not think Soapy did it. He later eats at a less expensive restaurant and cannot pay for it, but the waiters just throw him out of the place. He attempts to speak to a young woman, thinking she will call the cops, but she just takes his arm.
Later, he yells outside a theater and tries to swipe a man's umbrella, but the man and admits that he had found the umbrella in morning in a restaurant and hurries away. Ironically, Soapy is arrested when he is standing outside the light of an old church, loitering only to make the decision to change his ways forever.

O. Henry wanted to have Soapy commit a series of petty crimes in the hope of getting arrested and sentenced to spend the harsh winter months in jail. The author saw that these petty crimes would need to have variety in order to keep the reader interested. Soapy could not just keep going into restaurants and then revealing he could not pay for what he had eaten and drunk. One of the things that makes "The Cop and the Anthem" interesting is the variety of misdemeanors Soapy either commits or attempts to commit.
First he goes into an expensive restaurant intending to order the best the place has to offer. O. Henry itemizes Soapy's prospective banquet in order to characterize both the man and the establishment. "A roasted mallard duck, thought Soapy, would be about the thing—with a bottle of Chablis, and then Camembert, a demitasse and a cigar. One dollar for the cigar would be enough." But the head waiter escorts him out after seeing the condition of his shoes and trousers.
Next Soapy throws a cobblestone through a plate-glass window and stands waiting for a policeman to respond to the crash. But the cop who arrives on the scene will not believe that the culprit would still be standing at the scene of the crime.
Next Soapy goes into another restaurant "of no great pretensions," where his clothing will not prevent him from being seated and served. "At a table he sat and consumed beefsteak, flapjacks, doughnuts and pie. And then to the waiter he betrayed the fact that the minutest coin and himself were strangers." But instead of having him arrested, two waiters toss him out onto the sidewalk.
Then Soapy pretends to be a "masher" with a cop standing only a short distance away. Soapy probably expects to get arrested for disorderly conduct or possibly even assault, but the young woman he approaches turns out to be a prostitute, although O. Henry probably never used that word in print. The young woman walks off with Soapy as if they are old friends, and he has failed for a fourth time to get arrested. He could hardly have gone into another restaurant after gorging on beefsteak, donuts, flapjacks, and pie. O. Henry specifies that Soapy consumes four heavy items in order to make it understandable to the reader that Soapy would have to give up his restaurant trick for at least long enough to digest what he had consumed.
Soapy decides to go solo on his next attempt at getting arrested. "On the sidewalk Soapy began to yell drunken gibberish at the top of his harsh voice. He danced, howled, raved and otherwise disturbed the welkin." But the cop who observes his performance decides that he is a college boy celebrating a football victory and leaves him alone. The reader may wonder how Soapy has managed to get himself arrested over the past years. Has he tried all these tricks before? Does he have other tricks up his sleeve?
As his last attempt at fulfilling his goal of getting arrested immediately, Soapy steals an umbrella right in front of the umbrella's owner—but it turns out that the owner had stolen the umbrella himself and was afraid to call the policeman who was standing right on the corner.
Not only is there variety in Soapy's crimes and attempted crimes, but there is a sharp contrast between the comical tone of the first part of the story and the ironic tone of the end. Irony is usually like something that would be funny if it were not painful or sad or even tragic. Soapy was funny at first, but he becomes pathetic when he remembers his better days and then gets carted off to jail for loitering and vagrancy.
Soapy will be released in a few months, but winter will come around again. If he has lost some of his former jauntiness and bravado, he might end up having to spend next winter out of doors, in which case he could be found frozen to death on his park bench in Madison Square.