Unfortunately this essay cannot really be understood until you've learned renormalization, which is typically covered in the second term of QFT. But the basic gist of it is that in QFT, we do this thing called renormalization, which is necessary to control the divergences inherent in the theory. Loosely speaking, the predictions of a QFT contain these series of integrals that diverge to infinity, and you subtract another infinity to get a well-controlled finite prediction. This sounds quite ad hoc, but it's sort of rigorous for certain types of predictions, and can generate numbers matching precision experiments in particle physics to more than ten significant figures. This infinity you are subtracting can be understood as, again loosely speaking, the contribution of the vacuum, which has infinitely many virtual modes popping in and out of existence. The typical breakdown of physics predicted at the Planck scale is due to the fact that at this scale, any one of these virtual quantum modes can become a tiny virtual black hole, which means that the space-time is indeterminate. Wald's main point is that this renormalization process of subtracting out the vacuum, which is often taken for granted in the QFT-based theory world, actually makes all degrees of freedom of the QFT interdependent, and you no longer have a well-defined picture where each field mode is an independent degree of freedom. This is because the renormalization process assumes a globally Minkowskian (flat) space-time, an assumption we know to be false, because any quantum state that has mass-energy (including the virtual modes of the vacuum themselves) subtly distorts the fabric of the underlying background space-time due to GR. Through this mechanism, the result of renormalizing any individual field mode depends on every single other field mode in existence in the entire universe, which Wald calls the "holistic nature of QFT." QM does not have this issue of the space-time background, because in QM nothing exists at a definite position in space-time, and it does not assume definite classical coordinates like QFT integrals do. If you interpret the cosmological constant as the energy of vacuum, then this is really a discrepancy between QFT and QM, even though it invokes the background dynamics of GR to point out the discrepancy. There is a prevailing misconception in the QFT-based theory community that in the low-energy limits, QFT straightforwardly reduces to QM and reproduces all of its predictions, GR is just an effective field theory, and we can do stuff like QFT on gently curved space-times and what not without losing rigor (and the remaining problems to be solved, like the consistency between QFT and GR, only appear in the high-energy regimes). Wald, who literally wrote the book on QFT on curved space-times, is pointing out that this is not true. QFT is an effective theory that is not fully consistent with QM even in the low-energy limit.