Get Day Of Week in bash script

Using a different %-specifier is the real answer to your question. The way to prevent bash from choking on invalid octal numbers is to tell it that you actually have a base-10 number:

$ DOM=09
$ echo $(( DOM % 7 ))
bash: 09: value too great for base (error token is "09")
$ echo $(( 10#$DOM % 7 ))
2

This works fine here

#!/bin/sh
DOW=$(date +"%a")
echo $DOW

You can also use to return the day name

 date +'%A'

Use %u. Like this:

DOW=$(date +%u)

From the man page:

%u day of week (1..7); 1 is Monday