This seems to a problem with the way Adobe has designed the application on OS X (we've never had Windows users with this issue). It's not very intuitive because no other Mac application acts this way. Go figure...
The problem is this: You've created your slideshow inside Lightroom and press the Export button. No matter what you try, the "Save" button is never enabled so you can't export anything.
Contrary to what you may think, the dialogue will not allow you to select an existing folder to export to. If you try that, the Save button will continue to be disabled. They only way to get the button to enable is to type in a folder name. That folder can already exist or be a new one. Either way, the button will enable. If the folder already exists, Lightroom will ask for your permission to overwrite the contents.
So as long as you always type in a folder name, existing or otherwise, the Save button should become active.