Dê uma olhada aqui , há uma descrição que marca você deve definir para desativar a notificação.
On the bottom of View Downloads window there is an additional link and two buttons.
Options link allows you to change Windows' default location for downloaded files and documents. Normally, all files and documents are saved to Downloads folder in your user profile folder. Click Browse... to select a different folder for downloads. Clearing the Notify me when my downloads are complete check box will disable Notification Bar for completed downloads. This suits for those users who don't like Internet Explorer window activating each time a download is complete. You can still manage downloads using Download Manager after clearing the check box.
Isso pelo menos cobre o mais irritante.