Postmortem: on a PDU with low Power Factor, why did all of our servers reboot?
pF is picofarad.

Now, Power Factor is misunderstood...

Mains voltage is a sine wave. If you plug in a resistor, like a heater, it will draw a sine wave current which is in phase with the voltage, this means current and voltage are proportional. This is the ideal situation for the utility, as it minimizes losses in wiring, transformers, and other distribution equipment from the powerplant to the user.

Other kinds of loads will draw current in different ways. For example an inductive load, like a huge induction motor as used in industral machinery or elevators, will draw a sinewave current, but it will have a phase shift relative to voltage. Older switchmode power supplies used in computers contain a rectifier followed with capacitors, so they will only draw current on the peaks. 

Both cases are far from optimum for the power utility, as your current waveform causes higher losses in their network. But they only bill you for the power you use, not the losses in their network. So they will want you to pay extra to recoup the lost power.

"Power Factor" is a single-digit measurement of how current strays from the ideal sine wave. It is not perfect, but it is useful.

SMPS computer power supplies convert a high DC voltage like 320 VDC into low voltages like 12V, 5V, 3.3V, etc. Current technology can do this very efficiently. The problem is how to get the 320VDC. You can use a rectifier from mains and a capacitor, but this will only draw power on mains voltage peaks, and have a bad power factor. 

Thus, a PFC (power factor correction) circuit is added. This is a boost converter which takes as an input the rectified mains voltage, and generates high voltage DC, while drawing power from the mains in a well-behaved sinewave fashion.

However, this is not 100% efficient. If the circuit is designed to be 95% efficient at full load, then at 10% load it will lose efficiency. It is reasonable to expect the manufacturer would make a compromise, and take a loss in power factor in order to keep efficiency high. In fact, at very low load, when the PC is in standby and draws like 0.1W, the power factor correction would most likely turn off entirely, as its losses would exceed the actual used power.

Anyway.

Power factor measures how much evil the system does to the mains and the utility, but you have to remember it's a factor. The actual amount of harmonics and badly-shaped current drawn from mains depends on how much power and current the load actually uses. Thus, a load with bad power factor, but which uses little power, is not a problem. The problem is loads which use lots of current AND have a bad power factor.


  Is it reasonable that under these circumstances, that plugging in an additional system should trigger a state of temporary power failure on the low-load systems? Or, does this imply that the PDU or the server PSUs are defective?


No, this is not reasonable.

When you plugged in the additional system, it drew an inrush current from the PDU. Maybe the inrush current was too much, maybe not, who knows. If the PDU can't deal with that, it is the PDU's problem. If it cuts power to the other outlets when one single outlet misbehaves, it is also the PDu's problem.

It looks to me like your PDU is crap. I mean, did any other servers in the datacenter but the ones on this PDU crash? Probably not.


  take corrective action (like artificial load) when a situation like this occurs.


An artificial load (like a resistor) draws power. This raises the power factor (by making the misshapen current drawn by your computers smaller in comparison) and it also raises your electricity bill. It is more eco-friendly to simply donate money to your utility.