Professor Derek T. Muller has collected the list of cases in which voters or candidates have filed lawsuits, arguing that Ted Cruz does not meet the constitutional qualifications to be President. They are in state court in Illinois, New York, and Vermont; and federal court in Alabama, Arkansas, Texas, and Utah. The list is posted in Muller’s “Excess of Democracy” blog. Thanks to Rick Hasen for the link.
We actually vote for presidential electors, not the party nominees, so I don’t see how there would be any legal standing here. Unfortunately, most states prohibit the names of the presidential electors from appearing on the ballots and instead put the party nominees there as placeholders for the presidential elector slate. This needs to change. It is technically up to CONGRESS to determine presidential eligibility AFTER the election. Abolish the primaries and have the various state parties determine their convention delegates by either their own convention or caucus.
I believe all these lawsuits relate to presidential primary ballots.