This is a good example of the importance of knowing you target audience. You may think that your target group is advanced users but there is always a fraction of the target group, which are beginners. In turn this means that you really need to consider the usability of the site regardless of how advanced you may think the target group is.
If you enter the URL in the new toolbar (2.0 beta) and press on enter key, you will go immediately to the correct site. I'm now considering to remove the address bar of IE on my laptop. Screen is not so big, so having some more pixels for the real pages would be nice.
Depending on your area it may also be the competition checking out if your site is in there :)
I would tend to think that HitProf's response is more accurate. I use this feature in the Google Toolbar all the time, I've not yet upgraded to 2.0 and probably won't until forced to do so, don't need the extras just yet.
webdevsf, have you been entering your URI into the toolbar? If so, and you've not filtered for visits from your IP then you may be seeing your own searches. Entering a URI in the toolbar presents you with four options (usually).
Show Google's cache of www.example.com Find web pages that are similar to www.example.com Find web pages that link to www.example.com Find web pages that contain the term "www.example.com"