Voting to uphold the law in its entirety were Judges Joel M. Flaum and William J. Bauer. Flaum wrote the opinion.ADDED: Here's the opinion PDF.
Judge David F. Hamilton dissented in part, saying he believed part of the collective bargaining law violated the First Amendment. Hamilton argued the state could not bar some unions from having their dues deducted from paychecks while it allowed police and fire unions to do so.
AND: The panel said it's well-settled that "use of the state’s payroll systems to collect union dues is a state subsidy of speech that requires only viewpoint neutrality." The law didn't target any particular viewpoints. It subsidized the speech of public safety unions but not other public employee unions, and the unions had argued that the speech of the groups that were subsidized would be more favorable to the party that supported the legislation and so Act 10 wasn't genuinely viewpoint neutral, but only the dissenting judge agreed.