Crontab: “Temporary crontab no longer owned by you.”

I reverted from Linuxmint 18 Cinnamon 64bit to Linuxmint 17.3 Cinnamon 64bit and can no longer create a cron job. I have separate root (/) and home (/home/my-user-name) partitions and left the home partition untouched when I did the 17.3 installation.

I was having all sorts of difficulties creating a cron job, so I installed gnome-scheduler and tried to create a cron job that way. I got a warning dialog box titled

"Warning: Working directory of executed tasks"

and the message content is

"Note about working directory of executed tasks: Recurrent tasks will
be run from the home directory."

I clicked OK and the job shows up in the terminal as follows:

$ crontab -l
* * * * * env DISPLAY=:0 /home/my-user-name/wallpaper_changer.sh >/dev/null 2>&1 # JOB_ID_4

My wallpaper does not change every minute as it should. The script runs just fine from the command line and produces no output. Permissions are 744 octal for the script. This all worked fine under Mint 18, but I had the script run just once a day. I set it to run every minute only for testing purposes.

If I try the normal cron job editing method, I get

$ crontab -e
Temporary crontab no longer owned by you.
Error while editing crontab

Then I get an empty nano buffer rather than the normal crontab template full of commented lines. When I try to write my nano buffer to file /tmp/crontab.lmuwIe/crontab I get this error message:

[ Error writing /tmp/lmuwIe/crontab: Permission denied ]

Finally,

$ ls -l /usr/bin/crontab
-rwsr-xr-x 1 root crontab 35984 Feb  9  2013 /usr/bin/crontab

Will I ever be able to create a cron job again?

$ sudo ls -la /var/spool/cron/crontabs
total 12
drwx-wx--T 2 root crontab      4096 Sep 25 03:23 .
drwxr-xr-x 5 root root         4096 Sep 23 00:05 ..
-rw------- 1 root my-user-name  188 Sep 25 03:23 my-user-name

@Gilles
Well I've made a lot of progress. I got rid of all the error weirdness by reinstalling cron. Now everything works just as it should when I use

$ crontab -e

except that the script I've been using for years doesn't run.

But another script does run; so I'm lost.

Here's what I've got right now:

$ crontab -l
* * * * * env DISPLAY=:0.0 /home/my-user-name/wallpaper_changer.sh
* * * * * date >> /home/my-user-name/crontest.txt

(I didn't include the 20-odd lines of comments that precede the cron jobs.)

The date job runs exactly as it should but the wallpaper_changer.sh job doesn't do anything. I've used this for years and now it doesn't work. The script works fine from the command line and used to work fine from cron.

$ ls -l /home/my-user-name/wallpaper_changer.sh
-rwxr-xr-x 1 my-user-name my-user-name 694 Jun  2 14:30 /home/my-user-name/wallpaper_changer.sh

$ echo $DISPLAY
:0.0

What's up with this?