I have a script for the same purpose too, but I prefer a black-and-white 1-bit palette for that fax look. Here's my version -- note that it uses graphicsmagick, img2pdf, optipng, and pdftk. Also enforces A4 so some of you may want to change that. For fun it's doing the page processing in parallel to speed up a bit with large documents.

    #!/bin/bash

    # Adds a bad scanning effect to PDF files.

    if [ $# -ne 2 ]; then
      echo 1>&2 "Usage: $0 input.pdf output.pdf"
      exit 3
    fi

    convertPage() {
      # PDF filename in first parameter, page in second
      file=$1
      page=$(($2-1))
      png=$(printf "pdf2scan-page-%05d.png" $2)

      # Convert PDF page to black and white PNG
      gm convert -density 300 "$file"[$page] +dither -rotate 0.35 +noise Gaussian -type bilevel -fill white -fuzz 90% -colors 2 $png

      # Optimize PNG
      optipng -silent $png
    }

    export -f convertPage

    # Read number of pages
    pages=$(pdftk "$1" dump_data | grep NumberOfPages | sed 's/[^0-9]*//')

    # Loop through pages and convert in parallel
    for i in $(seq 1 $pages)
    do
      echo "$1":::$i
    done | parallel --eta --colsep ':::' convertPage {1} {2}

    # Create PDF from PNGs
    img2pdf -o "$2" --producer "" --pagesize A4 pdf2scan-page-*.png

    # Remove temporary files
    rm pdf2scan-page*

For a cleaner 1-bit look without noise and rotation, use "gm convert -density 300 "$file"[$page] +dither -colors 2 -type bilevel -fill white -fuzz 40% $png".