Tami-Lynn is Robert's mother.
Just because it'd make sense in Seth MacFarlane's world.
His impassioned rant about how awesome Apache helicopters are strongly hints at it.
Ted never existed.
One of two scenarios occurred: Young John is dreaming the whole movie after making his wish and seeing how life turned out if Ted came to life. The other scenario is that John is an adult who carries his teddy bear around and everybody seems to humor him by pretending the bear is alive.
The magic in Ted has regenerative properties
That's why Ted has no wear and tear after all these years - he walks around for over 20 years without shoes and his feet don't wear out, there are no old fixes and seams on him, etc. (These don't count for the end of the movie because it was connected with a new wish
John is a reality warper.
Where was the wish star when he hoped Rex had Lou Gehrig's disease.