What additional issues can be encountered when restoring/migrating a Network/Multisite install?

Firstly, if you’re not sure if you have a WordPress Network/Multisite install, then you very likely do not. They involve extra work to set up, and new concepts – you’re not likely to have one without knowing about it. (See here).

Multisites can get very large. You need to have adequate web hosting to allow manipulation of your multisite’s files and database. The main danger is of timeouts, especially on budget hosting with larger multisites.

Potentially, there are all kinds of strange and exotic options that you may have in your wp-config.php file. Typically, there aren’t.