I watched this awhile ago (take a guess how), and I almost want to take offense at saying we won't get the Dragon-Tiger thing, but then I thought about it for .3 seconds, and realized most people won't.
However! You underestimate anime fans.
If we're watching Toradora!, then chances are that we've all done at least a little research, whether overtly or when looking up an anime, and probably know at least some of the reference about Dragon's and Tiger's, even if it only extends to the point of knowing that the two interact, and are entwined in Myth, even if one doesn't know any of the actual stories (Shamefully, I haven't read enough japanese myth to get anything more than "They are connected." I need to move on from Norse Mythology, I've been on it awhile, and it's time to go to the next culture... which is Egypt. Damnit.).
Wow. I sound really bitchy here. I sincerely apologize.