How do I fix a mismatch between processor Architectures?

To me this looks like the Interop.Domino Library you're referencing is specifically for 32bit (x86) programs. You can either try to find a 64 bit version of the library and reference that instead or change the compile type of your programs.

You can do this by opening the properties page for each of your projects and setting the Platform target to x86.

You might like to create an X86 Configuration in Configuration manager first, partly to test it out on and partly so it has the right name when you look at it later.

Hope this helps