Global, network-wide shortcodes or text replace functions

To have a Network enabled shortcode, you only need a Must Use plugin. Just create the folder /wp-content/mu-plugins and drop your code there. From the Codex:

  • Always-on, no need to enable via admin and users cannot disable by accident.
  • Can be enabled simply by uploading file to the mu-plugins directory, without having to log-in.
  • Loaded by PHP, in alphabetical order, before normal plugins, meaning API hooks added in an mu-plugin apply to all other plugins
    even if they run hooked-functions in the global namespace.

The search and replace issue seems a bit more sensitive and maybe this plugin can be of use: Search and Replace and do it only in the post_content field. You can also use the filter the_content, search this site for various examples on how to deal with it.