I just read the opinion. This probably isn’t very helpful, but here are some quickly-assembled thoughts nonetheless.
The first thing to know is that Judge Bolton’s opinion is based on a preemption theory. That is, her view is that some of the sections of the state law are preempted by federal immigration law. The gist of preemption that under the Supremacy Clause, federal law trumps an inconsistent state law. Unfortunately, I can’t say very much about whether Judge Bolton’s opinion is persuasive or not because I’m not sufficiently familiar with preemption law or the details of federal law at issue.
Specifically, Judge Bolton construes some of the vague provisions of the Arizona law; concludes that those sections are inconsistent with the general concerns underlying the federal immigration policy; and then she blocks those sections from going into effect. The key precedent Judge Bolton relies on — and thus the place to start if you want to know more — is Hines v. Davidowitz, 312 U.S. 52 (1941).
Given that parts of Judge Bolton’s opinions are based on a statutory interpretation that the lawyers for Arizona themselves rejected, I would guess there is a possibility that this opinion may ultimately lead the Arizona legislature to pass amendments to the Arizona law clarifying some of the sections. But that’s just a guess.
Anyway, sorry I can’t be more helpful in evaluating the correctness of the decision: You’d really need to know a lot more about preemption law and federal immigration law to speak on that with any authority.