This is a great idea. I'm a scientist who uses Evernote as an easily searchable lab notebook that is accessible to (and sometimes editable by) labmates and collaborators, and it's very important to me to have the ability to prevent accidental or intentional modifications of scientific records. The read-only feature would also help to ensure that notes remain in chronological order, whereas now, an accidental keystroke while reading an old note bumps it up to the top of the notebook, making it harder to stay organized.
Finally, much like writing lab notes in pen, allowing users to make a note read-only (especially if it could be done automatically after some time interval) would help to build confidence in scientific integrity by alleviating concerns about fudged data; descriptions of methodology tampered with after the fact; and inadvertent, uncaught deletions of records and results.
I love your product, Evernote, but I'm always keeping an eye out for alternatives with similar functionality plus the ability to lock notes. If you added this feature, I would be much more likely to stay.