I believe Feynman was basically mistaken about the second point, though of course the field was brand new at the time - it is certainly possible to simulate the measurements of quantum mechanics to arbitrarily high accuracy on a classical computer with pseudorandom number generation; if you replace the pseudorandomness with a physical random number generator, then it might even be formally equivalent to a quantum computer (I think that's an open question, haven't tracked the developments in a while).

"Negative probabilities" is not quite right - towards the end of his life Feynman wondered about generalizing probability but that was just about intermediate calculations: he declared physical events cannot have nonnegative probabilities (in the same sense that physically I can't have negative three apples, -3 is a nonphysical abstraction used to simplify accounting). Negative probabilities are not part of modern quantum mechanics, where probabilities are always nonnegative and sum to 1. Quantum states can have negative/complex amplitudes but the probabilities are positive (and classical computers are just as good/bad at complex arithmetic as they are any other).

The "hidden variables" comment makes me think Feynman was actually a bit confused about the philosophy of computation - a classical computer cannot simulate how a quantum particle "truly" evolves over time, but that's also the case for a classical particle! Ultimately it's just a bunch of assembly pushing electrons around, that has nothing to do with a ball rolling down a hill. Computers only have Schrodinger's equation or Newton's laws, which don't care how the motion "truly" works, they just care that the measurement at the end is correct. If a computer gets the correct measurements then by definition we say it simulates the phenomenon.

Edit: clarifying this last point, Newton’s laws do have a known “hidden variables” theory in the sense that we know how an ensemble of high-temperature quantum particles can “average out” into Newton’s laws, there is an electrostatic theory of mechanical contact, etc. This does not (and seemingly cannot) exist for quantum mechanics, but merely having a quantum computer wouldn’t by itself help us figure out what’s going on: the output of a quantum computer are the “visible” variables, aka the observables. The fact that quantum computers are truly using the non-observables, whatever those might be, seemingly cannot be experimentally distinguished from a sufficiently accurate classical computer doing numerical quantum mechanics. If it turns out there is experimentally a serious difference between the results of quantum computers and classical qubit simulators, that would suggest an inadequacy in the foundations of QM.