For example, lecture B discusses the impossibility of precision local observables in quantum gravity, such as rest mass, using the following argument. Quantum mechanics gives us the limit of the uncertainty principle, which is to say that an infinite precision measurement of position requires an infinite amount of energy. On top of this, gravity tells us that the infinite apparatus required to measure a mass would confront the limits of Planck scale physics. With finite resources, infinite precision is clearly impossible.
What is wrong with this argument? Firstly, no one seriously denies that, in practice, finite resources are all we really have. This does not mean that there exists no theory capable of computing the rest masses to high precision, but this theory must circumvent the argument above. Observe that it was first demonstrated that quantum gravity could not be a local spacetime theory, and then we discussed experiments taking place in a classical spacetime. So logically, the argument cannot hold as it stands, once we have abandonned the local point of view, no matter how compelling it sounds.
The computation of rest masses is an important aspect of quantum gravity. It is true that the description of such observables should not impose a unique and universal spacetime. So in quantum gravity, when we measure the rest mass of a particle, we carry with us several strict experimental conditions that limit our capacity to draw resources from the apparently objective spacetime. An example:
Observer spacetime construction: our status as an observer living roughly $13.5$ billion years after the big bang, a cosmic epoch by which the varying $c$ cosmology sets a mass scale that limits our ability to probe vastly different scales (note that this does not imply that humans have a special status, only that they must be considered as observers with limitations).
One enjoyable feature of these excellent (albeit stringy) lectures was the stress on the interconnectedness of the outstanding problems, over all physical scales. Arkani-Hamed says, for instance, that a leap in our understanding of quantum mechanics, or any theory that supercedes it, must involve cosmology and other domains of physics. I wholeheartedly agree.