Excellent job, Jay. You really took him apart point by point.
Here are a few more minor errors:
"Most often the remote-update feature was used during manned missions to read up a refreshed state vector, integrating information received from the ground-based tracking tracking network. This was very helpful, but not strictly necessary. It enhanced mission success, but was not required for it." [duplicate word]
"This is too simplistic. First, Burns' 90-percent guess from the previous poitn is now taken as gospel." [misspelling]
"If we hypothetically set the reliability of PGNS to two nines (p > 0.99) and the reliability of AGS to three nines (p > 0.999, owing to its simpler design), then we that probability of failure, pf, is 1-p in each case." [I think you want to delete 'we']