I'd like to set permissions so that my Officers can create new thread tags. When I set 'feature access' so that 'Forum Administration' is set to Officer and above. Still, they are unable to create new thread tags.

What have I missed?

Cheers,

2 steps you need to do.
Sound like you did the first step. You need one more. Under feature access you also need to give anyone you give advanced permissions to the following:
menu | Administration Menu
Without that option they can not see the menus they need to be able to create a tag.

But I looked at my own site and Forum Moderation doesn't allow them to make Thread Tags.

So this begs the ultimate question. What if any feature access gives anyone the ability to create thread tags? Why isn't under forum moderation or administration. I would vote for adding an option to create a forum administration access level.

This bug has been fixed. Those with "officer - Forum Administration" security will now be able to do thread tag changes.