Bash - Escaping SSH commands

If both sides are using bash, you can escape the arguments using printf '%q ', eg:

ssh [email protected] "$(printf '%q ' mv -v "/home/dan/Downloads/complete/$dir" /home/dan/Downloads/downloaded)"

You need to quote the whole expression ssh user@host "command":

ssh [email protected] "mv -v /home/dan/Downloads/complete/$dir /home/dan/Downloads/downloaded"