There are two paths by which you can prevent a shared note from being edited.
The first path is to control the settings with which the note is shared. In the Add a Collaborator dialog:
When a note is shared, the collaborator permissions can be modified at any time using the "Add Collaborators" dialog
Changing the permissions to "View-only" means that the user who has the note shared can't make any changes.
The other option is to lock the note from being edited. This can also be useful even when a note isn't shared. To lock a note, click the "Note Options" menu and select "More options." Then, after picking "Lock note," the appearance of your note will change, with a lock icon added and the note title being grayed out:
The appearance of this note when it is locked
To unlock a note, follow the basic sequence: Note Options -> More Options -> Unlock Note.