Sorry I missed this earlier, Schultz.
Disclaimer: I have no in-person experience with the APA.
They are an independent church not in the Anglican Communion (so strictly speaking they're not Anglican).
To try and answer your question, Schultz, they're halfway between Anglo-Catholic and early-1960s mainstream Episcopal, a spectrum with some on the Catholic end (which explains why they quasi-officially accept Tract 90). 1950s-ish sort-of high church, not Catholic but obviously not like other Protestants either. Nice old-fashioned services with the priest facing the altar like an Orthodox or traditional RC priest, pretty much following the 1928 American Book of Common Prayer (1500s thous and thees, and Cranmer's and Coverdale's sonorous prose).
A word about their background helps you understand why they're that way.
They didn't begin with the 1970s Anglo-Catholic breakaway churches called 'the Continuum'; they hooked up with that much later, in the 1990s.
They began as a kind of conservative 'Dixiecrat Episcopalianism' in 1968 called the American Episcopal Church
. (There was another, more Protestant group of this kind, the Anglican Orthodox Church, nothing to do with Orthodoxy, started in North Carolina in 1963 by James Parker Dees. They're still around, microscopic and now high-churchified as they've become close to the Continuers.) This was when all the American mainline Protestant churches got much more liberal. (The Presbyterians seem to have really split in two; the conservative Presbyterian Church in America is thriving AFAIK alongside the liberal mainline PCUSA.)
There was an attempted merger with one of the Continuing groups, the Anglican Catholic Church, in the 1990s that ended quickly and badly; I'm not sure why. They started with two churches and ended up with three. Most of the old AEC became the APA. The Anglican Catholic Church remained and the third one is the Anglican Church in America (IIRC the name of the ill-fated merged church).
The top brass of TAC are keen on union with Rome but on their terms (their own bishop and I think married bishops); the ACA not so much - American Anglo-Catholicism was always less RC-orientated than the English version.
(Sidebar: the AEC's founding bishop, Anthony Clavier from England, had an Anglo-Catholic background but after the failed merger left his own church for some reason, converted to mainstreamish semi-liberalism and is now an Episcopal priest serving a parish in Indiana. His son Mark is an APA priest.)
There's a 19th-century denomination called the Reformed Episcopal Church, also not in the Anglican Communion, that broke away from the Episcopalians as a reaction against Anglo-Catholicism (which actually wasn't that big in the Episcopal Church).
Lately they've come in contact with the Continuing churches and have reinvented themselves as more like pre-1960s Episcopal; before they were more like Presbyterians (which is what ultra-Low Church of England was like).
I bring them up because the APA almost merged with them a few years ago, and just now one of the APA's bishops quit and is trying to take his diocese into the Reformed Episcopal Church (granted we're probably talking about only a few dozen people).
Chances are most APAers believe the elements in Holy Communion are not
completely changed into the Body and Blood of Christ like Rome and the Eastern churches do but do believe in a change and in a lasting presence after the service is over, a classic middle-of-the-road Anglican position.
The kicker, and I'm not sure what they believe on this, is if they believe in an infallible church. Anglicanism's Articles of Religion in Articles 19 and 21 say the church is man-made and fallible, a Protestant position. If that's what they believe then they're Protestants just like their liberal cousins the Episcopalians.
...when Anglo-Catholics say Mass they generaly do it with much more dignity and reverence than the modern RC.
prodromas is right that Orthodox usually don't talk about 'validity' outside the church, which they see as the Orthodox Church. Everything outside the church is a permanently undefined grey area. In practice both Eastern churches out of communion with Orthodoxy and Rome, the apostolic churches, are quasi-recognised (chrismations and ordinations are accepted economically upon conversion to Orthodoxy); Anglican and Continuing churches, even though they can be very close to Orthodox beliefs and practices, are not (their ex-clergy if approved for service are always reordained).
In the 1920s and 1930s some Orthodox patriarchates (Constantinople and Bucharest for example) said if the whole Anglican Communion stopped being Protestant and joined the Orthodox Church their clergy would be received in their orders. (I understand that's what the founding first hierarch of ROCOR, Metropolitan Anthony, believed.) As Anglicanism is mostly liberal and conservative Protestants obviously that never happened.
Rome doesn't recognise Anglican orders.