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TL;DR: Nationally, the Anti-Masonic Party was a single-issue party, but at the local level, they held a variety of other positions. Mostly, these were anti-Jackson positions, often allied with the National Republicans, but not always. There were often important differences, and the National Republicans, including their presidential candidate Henry Clay, refused to openly denounce Freemasonry.

William Wirt was nominated because, despite being a Mason who had never left the organization, he hadn't been active in thirty years, and he was willing to go on record to oppose with force of law the Masons, so long as that opposition was legal and Constitutional. Further, Wirt's nomination was a hope that the National Republicans would subsequently nominate him, too, to form an anti-Jacksonian union ticket, but that didn't happen. The two parties couldn't bridge the anti-Mason issue. Wirt regretted his acceptance of the nomination, but didn't withdraw, either, out of fear an alternate Anti-Mason candidate would better help Jackson get re-elected. Instead, he just did nothing.

The Anti-Masons and National Republicans worked together to try to prevent a "spoiler effect", but Jackson was popular enough he breezed to victory. Wirt only won Vermont, probably because Clay's platform was particularly unpopular there at that time, and there wasn't any significant support there for Jackson, either.

Full answer:

In this answer from a few years ago, /u/CoachZed lays out the motivations and most of the historiography of the Anti-Masonic Party. I think it's useful to read that answer as a jumping off point for my own below, which is based on one source CoachZed summarized (William Preston Vaughn's The Antimasonic Party in the United States), and a couple more sources not cited there.

The couple other sources are the chapter "Antimasonry Goes Political" in the book The Concept of Jacksonian Democracy: New York as a Test Case by Lee Benson (1961), and the chapter "The Antimasonic and Know Nothing Parties" by Michael F. Holt, found in the book History of U.S. Political Parties, Vol. I: 1789-1860, edited by Arthur M. Schlesinger, Jr. (1973).

Holt also wrote the incredibly-detailed and well-regarded The Rise and Fall of the American Whig Party, perhaps the history book on the Whigs. In the early part of that book, he cannibalizes much of his earlier chapter from the Schlesinger book when talking about the Anti-Masonic Party.

That out of the way, to answer your questions:

Was the Anti Masonic party actually far less of a single issue party than the name would imply?

Yes and no. According to both Benson but especially Holt, the Anti-Masonic Party certainly did start out as a one-issue party. And that issue, of course, was that they were against the Freemason organization. They wanted Masons out of government, the organization broken up, its members to resign from the organization, and so on.

However, with its early success in some local races in 1828 and 1830, it did what many successful "third parties" do in the United States. It filled a void left by the two major parties. It appealed to voters uncomfortable or disillusioned with the other two parties. And its Anti-Masonic mission lent itself to a specific set of principles.

First and foremost, it was a populist movement, appealing to Northern working class people: farmers, factory workers, and other laborers. The underlying assumption of the party was that the Freemasons were a secret society working as a cabal of elitists, aristocrats, oligarchs — 1%-ers, if you will. They believed the Masons controlled political offices throughout the country, gave preferential treatment to their fellow Freemasons, and generally undermined the democratic principles of free government. The U.S. was supposed to be based upon egalitarianism, on equality, and Freemasonry ran counter to this, by freezing out those who Andrew Jackson called "the common man".

In the lead-up to the election, on August 7, 1832, the Anti-Mason supporting newspaper, the New York Whig, laid this out in an editorial:

"It has been a reproach to our [Antimasonic] cause that it takes first among the lower classes. They are not wise who believe this and fail to examine its character; for in this country the lower class are at the head of all. The PEOPLE are sovereign."

More comprehensively, the Le Roy Convention of 1829 adopted an "Anti-Masonic Declaration of Independence", which you may want to consult, and can be read here. The gist is that the Masons represent an extra-governmental, international organization that undermines democracy and the rule of law. It's up to the people to exercise their rights and take back control of the government.

So, beyond being anti-Mason, the guiding principle was equality — for white males, at least. Equal rights. "Egalitarianism," as Holt puts it.

The other prevalent belief, as CoachZed's answer described, was an emphasis on Protestant Christianity. They weren't outwardly a Christian movement necessarily, but much of their membership were what we might identify as the "evangelical vote" today (although in their case it was mostly Mainline Protestants, not Evangelical Protestants). The belief was that the Masons, and other such secret societies and fraternal orders of the period (and there were many), as well as Catholics, were moving U.S. society away from being a Christian society, into a more secular society, and for the worse. Vice was taking the place of virtue. Men were more interested in fraternizing with their fellow Masons, partaking in "idleness" and "intemperance" (as the "Anti-Masonic Declaration of Independence" put it) than studying their scripture and reading their Bible at home with their families.

The one change in government that most Anti-Masons pushed for that didn't have to do with Masonry was that they wanted an end to mail delivery on Sunday. Congress had authorized the U.S. Postal Service to deliver mail seven days a week, which the Anti-Masons saw as a step away from piety and toward debauchery.

If you know a bit about pre-Civil War politics, these two main tenets of the Anti-Masons—democratic enfranchisement and religiosity—may make it clear why neither Andrew Jackson's party nor Henry Clay's party wholly appealed to the Anti-Masons. The Anti-Masons believed in that "Jacksonian Democracy" principle of government run by, and elected by, the "common man", not the elite. Clay's National Republicans (this was before the Whig Party formed) were still perceived as being beholden to those old Federalist Party principles of government unapologetically run by an elite class of Americans — not by "mob rule". Government offices should be awarded to those men who went to the right schools, came from the right families, and were otherwise part of high society.

But on the other hand, Jackson's Democrats were perceived as the more secular party, and more prone to vice. They were certainly the party that invited in the Catholic vote, the immigrant vote, and the urban vote (especially in the North), which alienated rural Protestants. Moreover, despite believing in Jacksonian "common man" principles of government, by and large, the Anti-Masons otherwise believed in Clay's "American System". That is, they weren't "states' rights" advocates. They were nationalists. They were republicans. (Hence, the Whig predecessor party's moniker "National Republicans".)

But even so, the Anti-Masons actually quite deliberately stuck to a nearly single-issue platform in that 1832 election, in order to broaden their appeal and stay united. At the end of Holt's chapter in the Schlesinger book, he includes the party's full 1832 platform, which includes 19 planks. Most of them are variations on what is wrong with the Masons and what to do about them, so they're not worth repeating in full, but I'll copy Plank 3 as the overarching theme of these:

"Resolved, That the organization of the anti-masonic party is founded upon the most satisfactory and undeniable evidence, that the masonic institution is dangerous to the liberties, and subversive of the laws of the country."

Three others are also worth reading, though, since they're the only other three that give any additional insight into the party's philosophy. Plank 6 is probably the most useful in understanding the party's membership (emphasis in the original):

"Resolved, That the direct object of freemasonry is to benefit the few, at the expense of the many, by creating a privileged class, in the midst of a community entitled to enjoy equal rights and privileges."

Plank 10 alludes to its Protestant membership:

"Resolved, That the oaths and obligations imposed upon persons when admitted into masonic lodges and chapters, deserve the unqualified reprobation and abhorrence of every Christian, and every friend of morality and justice."

And Plank 15 reinforces the party's commitment to democratic government, and the importance of the exercise of their right to vote:

"Resolved, That, in applying the right of suffrage to effect the suppression of freemasonry, we not only exercise a right which is unalienably secured to us, but discharge a duty of the highest obligation, in thus endeavoring to abate a great political evil."

Beyond this, as a national party, the Anti-Masons were pretty much silent. Instead, they left it to local county organizations to adopt their own, more specific platforms on the important issues of the day, whatever they thought would help them win locally. If that meant being more in line with Jackson's Democrats, then they should do that. If that meant being more in line with Clay's National Republicans, then they should do that instead.