Born in Year of the Snake, so invisibility.
After that, horse Horse HORSE.
A broken watch is only broken because a person perceives it to be. Unless the ancient Chinese mystics had 20,000 variations of Timex to program into their magic rock, I'm betting this puppy (er, horse) works like a good genie's wish. That is, acts off the intent of the wielder.
Another interesting bit is that even if Jackie doesn't know how to fix something, as long as he knows how it should end up, the object is "fixed" in spite of the gaps in his knowledge.
Basically, it doesn't fix things that are broken, it recognizes things I think are broken and reshapes them according to my ideals.
Control over my perception of reality becomes control over reality itself!
*insert maniacal laughter here*
My snake talisman is broken. I can be seen in the infrared spectrum, so I'm not really invisible. *fix*
My skin can't generate an invisibility field on its own. *fix*
My knees are broken from years of abuse. *fix*
My insides are broken; cancer and infectious disease stop me from functioning normally. *fix*
The fact that my body is allowing itself to slowly die out, that even if I "fix" a burn, my skin is still vulnerable to further immolation, that my life can be snuffed out from as little as a small piece of lead, is sufficient to conclude that my body is fundamentally flawed, i.e. "broken". *fix*
The main limit to the Horse talisman seems to be that it requires a physical presence to act upon. One can't *fix* war, or famine, or disease, but one can travel the countryside changing the minds of soldiers, rendering the land fertile, and healing the sick on their deathbed. One could also *fix* formulations of medicines that don't work as intended, and rely on existing distribution channels.
As long as the idea of what should be is clear, the machinations themselves are left to magic. How do I mend a broken leg inside of three seconds? No idea, but I know that a broken leg is broken. *fix*
This theory also explains why the Snake talisman also hides your clothing (it's part of your perception of "you"), why something like a Ninja Turtle would still say "Cowabunga!" (the toy should act like the person it's made out to be, regardless if the user even knows what a Ninja Turtle is), etc. The Dog talisman works the same way: What does immortality mean? Can't die, can't be mortally wounded, depending on personal definitions. How does immortality work? Magic.
One way it could be disproven is to find someone who has never worn clothing, or dress a person in clothing so strange it doesn't even register as such. If the "not-clothing" the thing the person doesn't perceive as part of him/herself, still becomes invisible, then there's evidence that the Snake talisman works off of something other than self-perception.