You got lost with what you're doing. Compare your script with this one.

Copy#!/bin/bash
# Still to come, see if the script runs with root privileges else exit

# Download FFMPEG static daily build and it's md5

# or exit if not
cd ~ || exit 2

# 1. get the file
wget https://johnvansickle.com/ffmpeg/builds/ffmpeg-git-64bit-static.tar.xz

# 2. Check the md5 is correct
if ! diff <(md5sum ffmpeg-git-64bit-static.tar.xz) \
          <(curl -L https://johnvansickle.com/ffmpeg/builds/ffmpeg-git-64bit-static.tar.xz.md5)
then 
    printf "%s\n" "md5sum doesn't match..." >&2 
    exit 1
fi

# 3. untar
tar -xf ffmpeg-git-64bit-static.tar.xz

# 4. and so on..
cp ffmpeg-*-static/ff* /usr/bin/
cp ffmpeg-*-static/ff* /usr/local/bin/
cp ffmpeg-*-static/qt-faststart /usr/bin/
cp ffmpeg-*-static/qt-faststart /usr/local/bin/
# Consider change second location to use ln -s
# Remove downloads and do some clean up

rm -fr ffmpeg-*

#EOF

A few fixes to your updated version. I removed your comments to make my own visible.

Copy#!/bin/bash
download_dir=~
dest_dir=/usr/bin/
version=ffmpeg-git-64bit-static.tar.xz
source_url=https://johnvansickle.com/ffmpeg/builds/${version}
md5_url=https://johnvansickle.com/ffmpeg/builds/${version}.md5

# You need braces to build blocks.
# As it was, your script terminated at the exit. Regardless. End of story.
cd ${download_dir} || {
    printf "%s\n" "You can't enter this folder." "Please change download_dir in this script..." >&2
    exit 1
}


if ! diff <(md5sum ${version}) <(curl -s ${md5_url})
then
    # Sum doesn't match is not really an error... I comment out the redirection.
    printf "%s\n" "md5sum doesn't match..." "Downloading new version" # >&2
    rm -f ${version} # >&2 -- Why would you redirect any output to stderr?
    curl ${source_url} -o ${download_dir}/${version} # >&2 -- Same as above.
else
    # You've done this already.
    # diff <(md5sum ${version}) <(curl -s ${md5_url})
    printf "%s\n" "Nothing new to download" # >&2 -- Why is this an error?
    exit # 3 -- I don't think this is any error. You checked and it's fine.
    # It might stay if you really MEAN it.
fi

# I'm not checking further.

tar -xf ffmpeg-git-*-static.tar.xz
mv ${download_dir}/ffmpeg-*-static/ff* "${dest_dir}"
mv ${download_dir}/ffmpeg-*-static/qt-faststart "${dest_dir}"

ln -sfn ${dest_dir}/qt-faststart /usr/local/bin/qt-faststart
ln -sfn ${dest_dir}/ffmpeg /usr/local/bin/ffmpeg
ln -sfn ${dest_dir}/ffmpeg-10bit /usr/local/bin/ffmpeg-10bit
ln -sfn ${dest_dir}/ffprobe /usr/local/bin/ffprobe
ln -sfn ${dest_dir}/ffserver /usr/local/bin/ffserver

rm -fr ffmpeg-git-*-static

Answers to your comment questions.

1. When is something to be determined as blocks?

   Here you can get a wider picture of blocks. In Bash they're called lists. Run this:

   Copyman bash | grep -A 30 'Compound Commands'
   

   and see what Bash's man has to say about them for a good start. This guide should be more approachable.

2. How to make it output the current running command to the console ex. the tar -xf etc.?

   The only ready solution I know for this is to run Bash in the debugging mode, if that's what you want. You can turn it on anywhere in the script with

   Copy set -x
   

   Then you turn it off with:

   Copyset +x
   

   You can do the same in the command line.

   You can also set the whole script to run in this mode in the shebang.

   Copy#!/bin/bash -x
   

   Or you can tell the interpreter from the command line to run in this mode,

   Copybash -x ~/bin/your_script.bash
   

I suspect that you are picking up another version of FFmpeg as John Van Sickle's FFmpeg does not show these error messages.

Try installing as follows:

mkdir ~/bin && cd ~/bin
wget https://johnvansickle.com/ffmpeg/builds/ffmpeg-git-amd64-static.tar.xz
tar xvf ffmpeg-git-amd64-static.tar.xz --no-anchored 'ffmpeg' --strip 1
source ~/.profile

And this should set you up with John's static FFmpeg for a local user! I tested this on my 18.04 system and it worked very well. Only remaining task would be to consider removing the archive remaining, if you have no further use for it:

rm ~/bin/ffmpeg-git-amd64-static.tar.xz

And that should do it...

References:

• Frequently Asked Questions: The FAQs for John Van Sickle's FFmpeg static builds with a few more installation options. I note that he does not use the ~/bin approach that I have described here.

In my CentOS 5.11 and FFmpeg 3.0, I have to use options

--pkg-config-flags="--static"
--extra-cflags="-I$HOME/ffmpeg/include -static"
--extra-ldflags="-L$HOME/ffmpeg/lib -static"

--enable-static tell a complier to create the "static libraries" (libav*.a). We can be combine FFmpeg API in the other standalone (static) application.

--disable-shared tell a complier not to create the "dynamically linked shared object libraries" (libav*.so). These type of libraries can be load and use FFmpeg API by the other application.

These 2 options doesn't complie FFmpeg as standalone static executable.