The only part I have a problem with is the part where police would ask people for their papers on "reasonable suspicion" that they are committing the crime of being in the country illegally. "Reasonable suspicion" is not exact enough and the definition varies. This could lead to legal residents or citizens of a certain ethnic appearance being singled out by police.
But this has already been brought up repeatedly. An alternate solution worth considering, I think, would be to make it standard practice to ask people about their residency whenever they are caught committing some other crime. Anything like traffic violations or whatever you can think of. And ask everyone, doesn't matter if they "look" illegal or not. This way those whose ethnic appearances more closely match that of the majority of illegal immigrants are not singled out or randomly stopped on the street to prove their legal residence. It helps solve the crime problem by catching and deporting illegals that commit crimes and forcing others to behave.
Two problems caused by illegals that are brought up are the crimes they commit and their use of social services paid for by citizens and legal residents. The above directly helps solve the first problem, but not the latter. Keeping illegal immigrants from taking advantage of state-provided social services would simply be a matter of requiring proof of legal residence whenever anyone wants to take advantage of such services. This could be extended as a requirement for all those who have undergone hospital treatment. Not only would this outright prevent illegals from using these services (and in the case of emergency hospital treatment, deport illegals after their treatment), but it would make it very difficult to live, and encourage them to leave. Indeed, this combined with the risk of being deported for committing even a minor infraction would be very discouraging for any would-be illegal immigrant.
So its possible to achieve the same results of the Arizona bill without the fascist "show me your papers" thing and the singling out of individuals with certain ethnic appearances.
Then there is the whole thing about making it impossible for them to be employed by any legit business.