In testing it to see what's going wrong, the script has logic errors. It's comparing a file name to a checksum, and that makes no sense at all... It's also exiting with failure places I'd expect it to be returning success. It's also not bothering to use a lot of its own predefined variables and just using hardcoded names in places.

You don't need to read raw md5sums out of the file anyway, md5sum can verify things by itself.

Code:

#!/bin/bash

# If we have no /tmp/.md5sum
if [ ! -f /tmp/.md5sum ]
then
        echo "Generating new checksum file" >&2
        md5sum /path/to/file > /tmp/.md5sum
        # Return error if .md5sum couldn't be created
        [ -f /tmp/.md5sum ] || exit 1
        exit 0
fi


# Check if file has changed, quit if it hasn't.
md5sum -c /tmp/.md5sum && exit 0

echo "File has changed, do things here" >&2

# ...
# ... ftp and stuf
# ...

echo "Generating new checksum file" >&2
md5sum /path/to/file > /tmp/.md5sum

exit

It might even be possible to check for multiple files this way, by doing md5sum file1 file2 file3 ... > /tmp/.md5sum, though you'd have to start processing the output of md5sum -c, not just reading its return value, to tell which files didn't match.

/tmp/.md5sum might not be the best place to store this file. Your homedir may be better.