I ran the fall river class III section at peak flow last year and it was pretty fun. I think is was a few thousand CFS (3000?) It felt like maybe a 4 mile wave train with random holes. In a 14' cat for a gauge the waves were maybe 12-15 high pretty consistently. I ran it in a kayak too and it was just a riot of big waves. I think the bottom rapid is called Bob's nemesis? not a huge deal, run left of the giant center rock at most flows, though there can be a right line for kayaks.
I've run it down to 280CFS in a playboat. the top is really shallow and a bit of a slog but the rapids are cool rock dodging and eddy hopping. Most rafters wait til about 800cfs+
There is a diversion dam about 3/4 of the way down. at lower flows you can run it rightbut it is intimidating. at higher flows rafts ran left of center. there is a huge slow lake above it and you are in no danger of finding youself suddenly facing a death drop unaware. Dropping the wrong line on it looks like certain death at most flows.
Other river characteristics: it starts in YNP. you can drive up to cave falls which can be a park and huck. the legality is questionable. I do know a guy who broke his back here. Not sure if it was bad line or sleeper rock.
Below cave falls there are some slide drops, notably sheep falls (yes, there are two sheep falls within 50 miles of each other). I think this stretch is rarely run due to brush and poison ivy?. It has been rafted above 1000CFS. I have heard the quality of the run is kind of blah. Definitely no major undiscovered vertical falls.