Next Fall I'll be teaching art history for the first time. I've got some great donations of slides from fellow profs, as well as my own photographs from museums, monuments, books, and websites - but I don't have permission for any of this, and at least half of it is probably copyrighted. How much can I do with it? I'd like to show it in class and put relevant slides up on the class (password-protected) website.
You can consult the Code of Best Practices in Fair Use for the Visual Arts to see if your uses are within the best practices of your field. For example, your peers have stated in Principle Two, "Teaching About Art," that teachers “may invoke fair use in using copyrighted works of various kinds to support formal instruction in a range of settings, as well as for uses that extend such teaching and for reference collections that support it,” given certain limitations.
You can use the Code as a guide as you consider those limitations. For instance, you may want to consider how you're linking your teaching objectives to your use of the work, make sure you're choosing size and other characteristics appropriate to the teaching objective, ensure that you're limiting access to the people being taught (your class's password-protected website might cover this), and, of course, assigning attribution wherever possible.
Once you've considered these limitations, you can make your own decision about how to use the materials you've gathered in your class. And if other school officials ask about permissions, you will be able to confidently explain your reasoning to them as well.