How should I check USB signal integrity?
There is no "good" voltage for the data lines, particularly when they're not connected. USB doesn't work that way (I'm assuming the voltages are 0 &lt; usb_V &lt; 5V. Anything else would indicate a serious hardware fault, which is outside the domain of your question). 

Furthermore, every hub actually receives, interprets and retransmits the USB data signals, so it's not like a bussed-network where all the data wires are tied together anyways. Connecting lots of hubs doesn't "affect the signal integrity" like that, since the signal is completely reconstituted by every hub in the chain.



My guess, assuming these are unpowered USB hubs, is that you're simply exceeding the allowed current draw of the USB host.  

Rather then look at the USB data lines, you should look at the USB 5V. It should be within a few hundred millivolts of 5V, and shouldn't have a lot of noise either.