Comment # 6 on bug 971885 from Egbert Eich

Felix, I've just retested this: setting the mode thru a script in
/etc/X11/xinit/xinitrc.d/ works on Intel as well. It is very obvious though
that the Plasma5 desktop will reset this to whatever has been configured in the
user session.
It is fairly obvious that first the mode configure thru 'xrandr ...' is set and
then changed when the screen settings application starts.

Adding a script to /etc/X11/xinit/xinitrc.d/ will however never affect any DM
as these scripts only run after the user has logged in.
This explains why you see the success /failure pattern in the list of comment
#2:
You get 1680x1050 on all systems which have this mode set before you run
'xrandr --dpi 108 --output ...'. It seems to be the preferred mode on these
systems and is also picked by your desktop. So you don't get this mode because
of your 'xrandr' command but because the screen setter of your desktop chose
this.

The 3 cases which fail have a mode of 1440x900 set - probably the limit for
this hardware combo. So your desktop will choose this as well - your 'xrandr'
command trying to set 1680x1050 most likely has failed anyway.
Running an 'xrandr -q' on one of these and providing the output here may shed a
lot more light on this.