Why was Yui's Heart the only SAO item to work in Alfheim Online? When Kirito enters Alfheim Online and notices his stats are from SAO, he quickly scrolls through the list of bugged items looking for Yui's Heart. He found it but it was renamed to something else, and when he used it, Yui appeared.

Yui's Heart was a very unique item in SAO as it was created from what Kirito could save of Yui after she was deleted. Since REC Progress made Alfheim Online based off of SAO, it would explain how all of Kirito's SAO items were bugged but Yui's heart remained and was renamed.

Why was Yui's Heart, the most unique item in SAO, the only SAO item in Kirito's inventory which wasn't bugged?
I'm going to answer this from a programmer's perspective.

When writing a video game, everything is built in layers, starting with simple IO (mouse, keyboard, sound, video), then a physics engine is integrated, and then base game mechanics added. 

Finally, the game itself is written on top of all this software.

All of Kirito's items would be part of the SAO game itself, and would be unrecognized item codes in another game.

However, Yui is a more integral part of the game engine, her program would exist in a earlier layer of the game. When the game was stripped down from SAO in order to make ALfheim, Yui's layer would have been left intact, allowing her to exist.

It is the same with Kirito's stats, they are more integral than the game items, and are programmed first.
(The fact that his stats transferred actually shows how sloppy &amp; lazy of a rewrite ALfheim was)

Side note: In a game as advanced as SAO or ALfheim, it is possible that items are created as needed by the engine (the Cardinal), every game would have its own set of items, with unique IDs.