When you click Verify, Bookdog sends a request to each of the websites addressed in your bookmarks. In accordance with internet protocols, the site responds with either "OK" or an error message. By analyzing the response from this response (if any) and the response from internet name servers given by your Mac, and using Sheep Systems' experience, Bookdog decides whether or not this bookmark has a high probability of being broken, and if so, formulates a diagnosis and suggested treatment.
Although we have trained Bookdog to juggle many bookmarks "in the air" while it is waiting for responses, Bookdog limits itself to 64. When more than 64 are outstanding, it waits until the number falls below 64 before sending any more. The internet port on your computer, and your internet connection, have a limited capacity of bits or packets per second.  If too many request packets are spurting out, the response packets will not be able to squeeze back in.
It may take several or tens of minutes if you have a slow internet connection or thousands of bookmarks. You may work with Bookdog's Main Window, or activate another application, or go take a break, while waiting for the verify process to complete.
[Technical note. The request Bookdog sends to each site is a GET request. This usually results in some useless data being received, although we cancel the connection to stop this as soon as the header which we need is received. According to internet protocols, Bookdog should be able to get the needed headers without the useless data by sending instead a HEAD request, and indeed this would eliminate the useless data and use less bandwidth on your internet connection. But we have found that about 2% of sites on the internet return an incorrect response to a HEADc request.]
You may adjust the rate at which Bookdog sends out its first requests to websites. The default rate of 20 requests per second (that is, 20 websites per second) works well if you have a single computer on a typical DSL or broadband cable internet connection; typically a thousand bookmarks can be verified in just a few minutes.
At this wicked rate, however, you will notice that the internet bandwidth available to other applications and other computers using the same internet gateway will be reduced. For example, Safari will load web pages more slowly and multi-player games played over the internet will "lag" until Bookdog completes the first pass of its verify operation. 
To reduce the impairment seen by other applications and users, lower the throttle setting and allow Bookdog more time to verify.
Slower computers will not be able to achieve 50 requests per second of regardless of internet connection; they will simply go as fast as they can. Also, if you have a dial-up internet connection, you will be able to complete only 2 to 5 requests per second. Although the overall verify time may be increased if the process is frequently waiting due to too many outstanding requests, setting the throttle too high does not affect reliability, because Bookdog re-tests all non-responding websites in a second pass, done slowly.
When the operation is complete, you may see the results by showing the Verify Bookmarks Report.