Does anyone knows how to set this? Vim will display the indentation symbol when wrapping a new line, When input it will disappear.
These options will make sure trailing spaces are displayed as dots (or whichever other character you set instead). As you say, the dots disappear once another character is entered, as the spaces are then not trailing any more. Look through other listchars options as well, if you want to see e.g. tabs or other cool stuff.
set listchars=trail:·
set list
(See :help 'listchars'
, :help 'list'
)