We will at least get some sort of useful error message to go on if it still fails: Try mounting the DMG on the command line in Terminal. Apparently there is an issue sometimes after opening too many dmg files, that is fixed with a reboot.
Reboot your Mac if you haven't already tried that. (There's an example of that in my screenshot below.) Or if you don't need to be logged in to the site to download the file and you want to be fancy, you can try curl -O url in Terminal to download the file. You can try downloading the file in a different browser as well. If possible, try downloading the dmg again, turning off any download assistant plug-ins you may have.
In most cases, the downloaded dmg file is actually corrupt or had an error downloading. If you see the 'no mountable file systems error' while opening a dmg, here's what you should try: The error was as the screenshot above shows trying to open a dmg (disk image), macOS showed the error 'no mountable file systems'. I didn't find a lot of good search results addressing the issue, so I decided to write up a post about it myself. I ran into an interesting macOS error while working with a customer.
