Thanks for the question. There could be a few reasons for what you are seeing:
(1) There could be a bug in ITensor! With the new release users have been inevitably running into bugs although most have not been too serious and I've been quickly fixing them. But if you could post your code I could run it to see if I can reproduce the "all over the place" fluctuations you report.
(2) There could be an error with the measurement code you wrote. I assume you regauged the MPS using psi.position(j) as you were doing the measurements, correct?
(3) Perhaps your wavefunction isn't converged but we'd have to look at that. What truncation error is DMRG reporting? Does this problem happen even for short systems or only as systems get longer? Does the energy converge to a consistent value by the last few sweeps? If the wavefunction is good then the correlation function measurements must be accurate too.