Maybe this belongs to the "other discussion thread" you mentioned, but I'm having similar problems to the user above.
I was quite happily using an older version of Pages until yesterday when I upgraded my iMac OS from Snow Leopard to Yosemite. The upgrade also updated my Mac apps, including Pages, which is the one I use the most. The previous Insert > Special Characters menu item now reads Insert > Emoji & Symbols and opens this:

However, when I try to insert one of the above emojis, I get the same result as the previous user (that is, just a blank space). After reading this thread, I googled, downloaded, and installed Symbola font and it now appears in the Font dropdown list in Pages. I notice that every time I double-click an emoji to insert, the font in my Pages doc is "AppleColorEmoji" and yet still, nothing is inserted. As you suggested above, I can select the blank space and change the font from AppleColorEmoji to Symbola, at which time the blank space is replaced by a black & white emoji. IMHO this is a very klunky way to use "emojis". I prefer the old way of inserting special characters. And I don't understand why I have a font called "AppleColorEmoji" when it apparently doesn't work.
But in the hopes that everything is fine and I'm just unclear on a concept, I'm throwing myself on your mercy...
Thank you in advance for any help.
~~Gay Alson