How would I test the continuity of an anti-static wrist band?
Overview:

A good wrist strap system has a large resistance between the skin contact and ground. Typically this is 1 MΩ, which is relatively large. This large resistance is there for your safety, in case an error somewhere connects you to a hazardous voltage. Even this high resistance is sufficient for protecting your devices from ESD. 

A typical multimeter should be able to measure this resistance. However, most continuity tests will probably report it as open. This is because many continuity functions are looking for resistances less than 100 Ω. 

Verifying your wrist strap:

Here is how you measure your wrist strap system - check from the skin contact side of the strap (red meter lead) to the part that gets connected directly to ground (black meter lead). Make sure your meter is configured to measure resistances higher than 1 MΩ, as the resistor will not be a precision tolerance. Note that in this picture I am making sure I don't touch any of the metal surfaces, which would give a bad reading.

Measure the resistance from the inside of the wrist strap to the outside or the end of the cord. Make sure you're on the high resistance scale of your meter if it does not auto range. 



In the labs I work in, the resistor is in the actual lead somewhere (the black wire). On the snap housing it is marked as 1 MΩ, and all the wrist straps are low resistance connections from the skin side to the snap connector. I have seen ESD straps with a 1 MΩ resistor built-in.

Don't use the continuity test:

For kicks and giggles, here's the result when you use the continuity check function on the whole thing - it reads as an open circuit (no continuity). With my setup, I would expect the meter to beep/show continuity on the wrist strap, but not on the wire lead.



Conclusions:

Without knowing if the reviewer just used a continuity test, or actually measured the resistance (or even where they measured), it's impossible to draw any conclusions from the review. If the reviewer knew how to properly measure the system, then I would consider that a defective product. If the reviewer tried to use a continuity check across a 1 MΩ resistor, then the reviewer is not being helpful at all. The wording of the review makes me suspect the latter, but it is impossible to know from what was written.