What is the "quality" of a Wi-Fi access point?

According to the documentation for Wireless Extensions, the information provided to Wireless Tools comes from /proc/net/wireless, which are more clearly defined by:

The basic difference between Quality - link and Quality - level is that the first indicate how good the reception is (for example the percentage of correctly received packets) and the second how strong the signal is. The Quality - level is some directly measurable data that is likely to have the same signification across devices.

It appears that the Quality - link value is the one that other tools tend to reference most.

It should also be pointed out that /proc/net/wireless is apparently a clone of /proc/net/dev which provides a different output, but you could in theory calculate the difference.

Looking at the source briefly, it appears these values come from the driver. That could explain your problem with the Quality - level and Quality - noise values: your driver doesn't support Wireless Extensions, or doesn't support it well.