We will not know for sure until we see how the law is actually enforced. For example, so new additions to the law were just passed yesterday that are supposed to make racial profiling less possible. We'll just have to see.
The major pro would be that the law could reduce the number of illegal immigrants in the state. If all states did this, it could reduce the number of illegal immigrants in the country as a whole. Many people think this would be good because they think the illegals cause there to be lower wages, more crime, more demand for social services, and other such problems. Many also think that the simple presence of illegals is an insult to the idea of playing by the rules and following the laws.
The main con, in my opinion, is if the law ends up being enforced in a way that harasses people based on the way they look. The law says police need to have a reasonable cause to think that someone is illegal. Will they do that based on skin color? On accent? On whether you can afford a nice car? What kind of evidence do you need to have a reasonable suspicion that someone is illegal. This is where we need to wait and see.
We also need to see if the police will make up excuses to stop more brown people just to check their ID. The police are only supposed to check in the context of enforcing some other law. However, we will have to wait and see whether they really stick to that rule.
This is a very timely issue and topic. The advantage with it being so relevant in real time is that the lists of pros and cons are more of analysis and conjecture than anything else. Few, if any, are going to be able to effectively call out the distinct pros and cons with anything of authority because of the "newness" of it. Certainly, if one believed in a strong "states rights" position, then this would be a positive. Arizona acted, presumably, because it felt that the federal government was not being responsive enough. This is an example of a state acting where it perceived the federal government to be ineffective. Along these lines, the Arizona immigration law is an active step in an arena where a politically sensitive base of people on both sides have created more talk than substantive action.
That being said, the law has really angered a great many people. The perception of racist based legislation has been raised as a significant talking point. It has moved to a point where athletes, who for the most part are a silent group in the fear of angering fans and sponsors, are taking active stances against such legislation. Vocal calls are being made for athletes to protest the upcoming All- Star game, to be played in Arizona in 2011. There is also some question as to whether the law is sustainable and if it will survive the legal challenges present.
Immigration numbers to Arizona are down, and some of the immigrants living there without papers have left the country or the state for places with less restrictive laws. So in the purest sense, some could argue that the law is effective, and achieved what Arizona voters wanted. You could also argue it's reasonable for a state or a nation to require proof of residency just like we require they have licenses and insurance for vehicles, or passports and visas to cross a border.
On the other hand, the law has cost Arizona tens of millions of dollars in lost tax revenue, from those immigrants living there and the money they spent/taxes they paid who have now left, and from other cities and states refusing to hold conventions and/or do business with Arizona because of their disapproval of the law. Discrimination in checking for residency status would likely be very common and biased against Latinos, whether citizens or not, and one could argue that a papers requirement is unconstitutional (and it probably is).