No Export for You: The Japanese Bonus Disc allows players to get Celebi, but for the American release, Jirachi was made available instead. PAL areas, however, didn't get the Bonus Disc at all (Jirachi being made available via Pokémon Channel instead). Players in both regions who wanted Celebi had no luck at all.
The only species snaggable in both games, not counting Togepi and Mareep, which were E-Reader events in Japan, is Makuhita. However, many families are in both: Swablu/Altaria, Houndour/Houndoom, Slugma/Macargo, Ledyba/Ledian, Piloswine/Swinub, Pineco/Forretress, Teddiursa/Ursaring, Spiarak/Ariados, and the Hitmons. Others can be obtained in both via trade or poke spots (in XD).
A shiny Pokémon from this game is one of the rarest shinies in the entire franchise. Shadow Pokémon can be shiny but it is impossible to tell until they have been captured whether they actually are. Any opposing Shadow Pokémon that appear shiny are almost certainly going to revert back to regular coloring once actually checked.