If you were a hemopheliac, someone whose blood doesn't clot when cut, you would want to avoid being tattooed. Also, if you were on any blood-thinning medications, even aspirin, it can make you bleed very heavily when being tattooed and that's not good either. Also, if you were sedated and physically unsteady (like drunk people often are) it can make for a bad tattoo as the client moves around unexpectedly and can mess up the artist. Plus alcohol results in the thin-blood, heavy-bleeding reaction as well.
