I want to suggest something like an issue tracker. It would have to work for tasks both large (year-long investigations) and small (arranging catering for a meeting).
The issue trackers I'm familiar with with are too software-development-oriented, or make too many assumptions about your "agile" religion. Are there any good options for non-engineers?
They use mainly Windows and have iPads. I don't like web-based tools, but that might work better for them because they don't have administrative privs on their machines. Something that also incorporates a wiki might be nice. There will be resistance if it's not really easy to use."