1. Drop down menu disappeared in the course list
2. Drop down menu in Learning Path course tool shows only "All Items"
Isue is fixed since LMS versions: 188.8.131.52 | 184.108.40.206
This is the Issue of IE 11. Older SPLMS versions hasn't been tested against IE11 and it's quite possible there'll be a number of issues here.
The temporary workaround is to switch IE 11 into Document Edge mode while enabled developer tools (F12):