This is an important feature a failed read can genuinely occur if a temporary file has been removed or if you try backing up a sysetm file in /proc /sys (which you shouldn't really anyway).
The way to fix this is the following switch:
--ignore-failed-read
Example:
sudo tar --ignore-failed-read -czvf mycomputer-backup.tar.gz --exclude=/home/otheruser/* --exclude=/proc/* --e........