I get an error saying "The root folder of your album hierarchy at Dropbox is missing or invalid"

Note the folder option you selected in the My Account section. This is where the plugin is asking you to specify a Dropbox folder where you keep your photos. This must be an existing folder. By default the plugin assumes you will be using the "Photos" folder, so it is the default option. Problem is, not not all users have the Photos folder. If that is the case, you can either open your Dropbox account in the web browser and create a new folder named Photos.

Alternatively, use the "This folder" option and point the plugin to any existing folder where you keep your photos. In the latter case, the folder can be anywhere in your folder tree. Just make sure to correctly specify its path, starting with slash. Example: "/My Stuff/Photos" points to a Photos folder inside a My Stuff folder, located at the top level.

The plugin is asking for Dropbox authorization and gets stuck on that window.

Automatic authorization is not working because your default web browser is unable to handle a special URL, which passes control back to Lightroom once the authorization is complete. You can solve this quickly by changing the Authorization Method to manual. You would need to copy and paste the authorization code between the browser and the plugin window, but at least you'd be able to authorize.

Here is an example of how to check your browser configuration to enable automatic authorization in Google Chrome:

1. Go to Settings > Content Setting
2. Make sure the "Allow sites to ask to become default handlers for protocols" is enabled
3. Put that URL in the browser's address bar: lightroom://com.alloyphoto.lightroom.export.dropbox and press Enter
4. Do you get a small pop-up asking whether you want to open that URL in Lightroom? If you do, select the checkbox to "Always allow"

Also, make sure to check out General Plugin FAQ.