The best uses seem to make use of the touch interface, so any remote control operation might benefit from dedicating an old iPad to it. Getting a sturdy goose neck or other type of iPad holder helps keep the iPad where you need it. Dedicating an iPad to one use means you don't need to keep upgrading it and the software on it all the time also (if it's network connected keep it on a private network rather than connecting it to the internet, so that you don't need security updates.)
Another application might be as data entry tablets. For example, when asking people to take a health survey you can run a simple app that asks questions and records answers and just hand it to anyone you ask to take the survey. (Not sure if iPad's can be easily sterilized for use in today's world. The touch pad might not like solvents.)