Any ideas why this would happen with just some FOLDERS?
(P.S. These are not "locked" folders I have created or OSX System Folders.)
Are you sure they aren't "locked". There are many kinds of lock.
In particular, the folders that are automatically created for you have an ACL (Access Control List) that says they cannot be deleted. They're not actually locked. You can add/delete items within them, and Get Info shows the "locked" flag unchecked.
But if you can't delete them, you also cannot rename them, because a rename is tantamount to deleting the old name and adding the new name.
Examples of such folders in your home folder are Library, Documents, Desktop, Downloads, Movies, Music, Pictures, Public, etc. They're not system folders, and they're not locked, but you cannot rename them.
This is not new with Yosemite, and not specific to the Magic Mouse.
Another possibility is that it's just a matter of timing. It takes several clicks to set up a text selection, and what happens depends on how much time elapses between successive mouse events. It's real easy to end up opening the folder or dragging the folder or its name instead of selecting text within the name if you get the timing wrong.