There is no way to enforce this law without harassing American citizens and legal residents. If a cop thinks you might be Mexican (or Canadian, or German, etc) you will be asked to produce your proof of citizenship, green card, etc. And, no, your driver's license is not proof of citizenship. If YOU (an American citizen) go out for smoothie and forget to take your notarized birth certificate and social security card, you can be locked up while they process your status.
Don't believe that can happen? It happens already... the only difference is now this new law REQUIRES the police to do it and encourages citizens to sue the police if they don't. It is going to be a godawful mess and will probably bankrupt some rural municipalities. If they try to uphold the law they will be sued by improperly detained citizens. If they fail to uphold it they will be sued by other citizens who still see too many durn Mexicans walking around. Its a no-win situation for the police (and any too tan citizen).
This is a big deal, and if you think it is not, I'll leave you with this final point: A major consulting client based in Texas just told me they are canceling their expansion into Arizona. The owner of the company is 3rd generation Hispanic American and about a third of his work force are either Hispanic, Indian, or Asian. Whether or not enforcement of this law becomes the debacle many of us suspect, the expectation of harassment is enough to cause major economic damage to the state.
There is a much better way to handle the problem of illegal immigration: Crack down on the business that hire undocumented workers. Have real enforcement with real financial penalties for the businesses that don't follow the rules (not the token effort and paltry wrist slap fines we have now). Without job opportunities, you remove the incentive for illegals to even enter in the first place.