On July 16, opponents of Arizona’s top-two open primary initiative filed a lawsuit in state court, charging that the measure violates the Arizona Constitution. The Arizona Constitution, like the state constitution of all states that permit statewide initiatives, requires that initiatives be limited to a single subject. See this story.
UPDATE: here is the complaint. The only group political plaintiffs are the committee formed to oppose the measure, and the Arizona League of Women Voters. The individual voter plaintiffs include Barry Hess, who has run for Governor of Arizona as a Libertarian. The Complaint charges that the measure violates the single-subject rule, and it also charges that the description of the initiative on the petitions is misleading.
On the single subject issue, the initiative abolishes elections for party officers. None of the three other states that have top-two systems (Louisiana, Washington, and California) abolished elections for party office when they started using top-two systems. There seems to be no necessary connection between a top-two system and eliminating elections for party office.
The top-two open primary initiative does not mesh with the existing public funding law in Arizona. The initiative does not attempt to alter the public funding law, but the public funding law assumes that the state has party nominations, and sets out different rules for public funding depending on whether a candidate is running in a district in which one particular party is strongly dominant, versus other types of districts. If the top-two law passes, it would be difficult to reconcile the public funding rules with the top-two system.