Probably the main recurring scene involves an extended conversation between Remy Marathe and Hugh Steeply on a hilltop overlooking Tuscon. Marathe is a legless French Canadian agent of uncertain allegiance and Steeply is a US agent posing as a female reporter called Helen. Closely following the back-and-forth between the two allows the reader to put together major aspects of the grand narrative of the novel.
My favorite scene was a one-off involving the younger kids (pre-teens) at a tennis academy playing an extraordinarily convoluted and physically intense game called Eschaton (think Risk played with tennis gear). If any particular thing made the 1,000 page slog worthwhile, I would say it had to be that.
The footnotes alone could have made up an entire book.