Maybe I'll have time to look up citations this weekend. But my recollection is that Hart questions the emphasis of Whitefield and other evangelists on the new birth (deemed a form of pietism--"Am I really saved?") and contrasts it with with the idea of being a member of the church in good standing formally affirming the confession. I was also thinking of things like Hart's denigration of prayer meetings and his advocacy of a prayer book.
I can't help but think that the kind of preaching you see in the churches like the HRC and FRCNA (and those heavily influenced by Puritan spirituality) and the experiential emphasis in the Reformation Heritage Study Bible (which is why I mentioned it) would make him uncomfortable and be seen as a sort of revivalism or pietism.
I seem to recall reading him asserting that the Old School Presbyterians were too tolerant of revivalism. They were certainly opposed to the Second Great Awakening, so what kind of revivalism were they too tolerant of?
EDIT: Much of what I was recalling is found in
this article of his in which he argues for "High Church Presbyterianism" in contrast to certain aspects of Puritanism and Old School Presbyterianism.