If the person to my right puts down an initial meld that is less than the required number of points but no one notices it until I have played my hand, what happens?
The exposed cards become subject to the usual exposed card penalty:
From section 55 of the rules (emphasis added):
If for the initial meld of his side a player shows less than the required count, he must validate his meld if possible with additional cards. If he cannot do so, or does not do so before discarding, all the cards he has exposed from his hand are dealt with under rule 54. If he has incorrectly taken the discard, he must restore it to the pile before making his own discard from his exposed cards.
If a player exposes one or more cards from his hand, except to make a legal meld, all such cards must be left face up on the table and discarded in successive turns, except that the obligation to discard lapses for each such card that is included in a valid meld (including its use to take the discard pile.)