1. The letters, the blogs within are sorted correctly from what I can tell.
Screenshot: https://cl.ly/XiWU
2. They’re all Uppercase first letters. If I put a lowercase first letter, your script seems to break (for instance, if I put iSimplePlayground -> your script adds a Capital I to the list, but no arrow to choose any options).
3. There are no duplicates of letters, they are all unique, but as you can see from the screenshot, it looks like there are two sets of letters both alphabetically sorted.
If I change SimplePlayground to ASimplePlayground, then an A appears at the bottom of the list.
4. This does not happen on my 3.8 WordPress installation at all.
5. The problem is not caused from any changes I made to your code, both your original code and my modifications work the same (not working correctly on 4.0, and working correctly on 3.8).