Ver. 4.07 b.1246 BETA 64-bit

When writing in a note, the insert key does not change to overwrite.

It works Ok in other programs.

Is this normal in AllMyNotes or is this a bug?

This is by design, the overwrite mode kind of old school feature and it's rarely used feature. As you can notice, it's also disabled in Chrome, Firefox, Thundermail, Google Docs, and many many other software titles. These days there is many other useful keyboard shortcuts and mouse gestures to quickly select/delete unneeded text. At the same time new users have no idea about this feature and when it turns on by mistake it simply drives them crazy as they don't know how to turn it off.