Hi, The owner of my boyfriend's company is conducting an "internet audit" and threatening to dock people's pay for time spent on the internet for personal use. Can he do that?

Pretty much, no. However, he could certainly be fired or otherwise disciplined.

An argument could be made that the employer only needs to pay based on actual hours worked and that time spent surfing the Internet is not time worked. Still, it is a weak argument with some obvious counter-arguments and I agree with Patty that it is a lot legally more straight forward to just discipline the employees. I have worked for employers who routinely fired people they caught doing such things.

I have worked for employers who routinely fired people they caught doing such things.
I don't know of any company that would not terminate employment for excessive personal use on the Internet.
JoeC