The Afiqomen must be the last item to be eaten on the night of Pesah at the Seder. One may not eat anything after it, not even fruit. The reason for this is that the taste of the Massa (Matza) must remain in one's mouth. The cups of wine of Birkath Hammazon and Hallel that are drunk after this are not included in this ruling. After this, however, one should not consume anything except water and, some say, coffee.
There are different opinions as to what one should do if he inadvertently did eat some other food after the Afiqomen. There are those who say he is not required to eat the Afiqomen again. However, the Eliyah Rabba states that if he has not yet made Birkath Hammazon, he must eat it again.
The Afiqomen must not be eaten in two different places. The reason for this being that it is in memory of the Qorban Pesah (Passover sacrifice) which had to be eaten in one place, as it says: "In one house shall it be eaten". The Maghen Abraham states that it should not even be eaten at two different tables in the same room.
(Shulhan 'Aruch 478:1 with Rama. Ben Ish Hai, Yr. 1, Parashath Saw, Oth 35. Kaf Hahayim ibid Oth 3-6)
