Partial pressures and oxygen saturation are hotly debated in high altitude mountaineering circles. During most of our expeditions we take pulse oximeters and take readings regularly.
In my experience people do not typically experience 'significant' altitude related discomfort until around 3,500 to 4,000 meters (11,500 to 13,200 feet). That said, recently a client on a Kilimanjaro trip I was asked to guide (thankfully I did not go as I was already commited to other activities) contracted cerbral oedema and died. They had only just breached 3,000 meters (9,900 feet).
Mileage varies and each individual is unique...the main priority should be to ascend in a slow and controlled fashion and to treat altitude related illness aggressively...drink and descend.
We had quite extensive medical support for our Everest 2003 expedition and had a couple of oximeters. Oximeters measure the level of oxygen saturation in your blood. They can be a basic indicator of high altitude acclimatization, though the readings they provide are indicators only and need to be taken in context.
We took readings all the way up to 7,300 meters (24,000 feet) and obtained some 'interesting' results. At sea level my oxygen saturation is usually 98-99% with a resting pulse of about 53.
The photo below is my reading after a day's rest at Camp III at 7,300 meters. My reading is 67% oxygen saturation with a resting pulse of 119. Big difference.
This was not my lowest score - I experienced the 'honor' of my lowest scores one night when I had frighteningly severe sleep apnea (when you stop breathing in your sleep). After being awake for some time I took my reading and it was 49%.
I can only begin to imagine what our readings where above 8,000 meters (26,400 feet).