No mistake that I can see. If you can cap the jar without it falling apart then it should safely hold a perfect vacuum, possibly even if it has a crack in the glass.1) Am I making some sort of mistake here?
There can never be more than one atmosphere of negative pressure, so preserving jars are very safe. Positive pressures must be avoided, but the cap and seal are designed to prevent positive pressures. Any other container will need to be carefully assessed.
No. The last two percent to a perfect vacuum are insignificant and quite safe. On the other hand, the last two percent with positive pressure will be as deadly as the last 0.1% because that is when the glass will shatter explosively due to the high internal pressure.2) Is that last two percent that much of a difference from essentially perfectly safe to "RUN FOR YOUR LIVES!"
Vacuum is inherently safe so long as you are not in it for long, and you do not stand at the end of a shock tube gun barrel. Air pressure on the other hand can be deadly with only a couple of psi, which is your internal pressure, and getting air under your skin can cause an air embolism with symptoms like the "bends". You should be able to suck a vacuum with your mouth down by 10 psi to about 4 psi absolute. You will not be able to blow 2 psi positive without embolism, probably of your salivary ducts initially, maybe followed by a stroke, depending on where the bubbles go.