Ted doesn't take much damage from John in a fist fight, but later gets "killed" due to cuts and tears. This is true for real stuffed animals. Because they have a spongy consistency and lack brittle parts, impacts do not harm them, but they can be torn apart fairly easily.
In the "Where Are They Now?" Epilogue, it's stated that Donny was arrested for kidnapping Ted, but the charges were dropped "when everyone realized how stupid that sounded." This is played for comedy, but it also implies that despite 27 years of Ted's existence, he's never been given legal rights. Taken further, it means that unless these steps are taken, others will be just as able to attempt to kidnap Ted without fear of repercussion.
How about that because of this, a man who very nearly committed vehicular manslaughter over a freaking teddy bear is back on the streets, and remains the caretaker of an already-damaged child who may or may not even be his son? I mean, hell, he didn't act like Ted was his first kidnapping victim.
Actually, that may have been his son that he had probably kidnapped from a wife or girlfriend that may have had custody of him.
Though they probably chose not to due to fear of being made laughing stocks of being the person who kidnapped a stuffed toy, which is probably Donny's fate.
John tells Rex that he hopes Rex gets Lou Gehrig's Disease. In the "Where Are They Now?" Epilogue, we find out that Rex did, in fact, contract Lou Gehrig's Disease. Since the entire movie is based on the idea that John brought Ted to life through the power of a wish, does this mean that John possibly gave Rex Lou Gehrig's Disease with another wish?