I can't replicate the problem you're having. I tried using both Firefox and IE but none of the links I clicked on the dropdowns opened in a new window. They all opened in the parent window (my strong personal preference).
Have you tried viewing your blog on another machine in case this is a browser/machine configuration effect?
Have you looked at your blog in another browser? If not, I'd strongly recommend that you do. Then you'll be prepared for your designer when s/he gets back in touch with you.
The Home page navbar in Firefox shows 8 page/section links + RSS. In IE, there are only 5 visible links + RSS. All 8 are there - it's just that 3 of them are invisible! If you move the mouse around the navbar, dropdowns start appearing all over the place - some of then very badly positioned
The dropdowns are almost unusable in Firefox. It took me 5 attempts to click on the March 2009 Archive link (at the top of the dropdown) because the dropdown kept rolling back up. And in both browsers, the Archive dropdown is extending well below the bottom of the browser viewport - making it impossible to access all of the archives.
Sorry to sound so negative but I think someone needs to have a few strong words with your designer. Especially if this is paid work.