There are some special secret and hidden items/weapons in the game. These do not include obvious/unspecial ones that you are bound to get by defeating enemies, opening chests, or recruiting characters in the main game. However, it may give hints to getting special/powerful weapons you may not get otherwise. Here are their locations.

Rapier: Visit the house in chapter 2 located in the middle of the forests with Shon.
Emblem Lance: Visit the house as mentioned above with Gordon.
Elysian Whip: Send a unit to the bottom of chapter 3 where the Pegasus Knights are (the cliff).
Talisman: Enter the odd, seemingly empty and useless room located in chapter 5 with any unit.
Killer Lance: Hunt down/defeat the cavalier holding a Killer Lance in chapter 5x.
SilverSword/DragonAxe: Trade Levion's inventory to either Althares or Kelik in chapter 12. Levion will disappear and rejoin later back with fresh equipment. Delphi Shield: Using Althares, steal the Delphi Shield from Lena in chapter 14.
Member Card: Talk to Tekun with Althares in Chapter 15.
Guiding Ring: Have Kelik or Anakin step/wait to the right of the pillar in the Respite from Battle.
Door Key: Have any unit stand next to the door/gate to the "shopping area" in chapter 17x where Liuke is. A door key (to open the gate, duh) will be found.
Sword Crusher: Using Althares, steal Ethan's elixir in chapter 18, and then make Ethan use a javelin by sending a unit two spaces away. Then defeat Ethan so that the Sword Crusher will drop from him.
Adamant Lance: Similar to above, but with Cid in chapter 19x, and a spear instead of a javelin.
Sylmeria: Select "no" when choosing whether Leopold will join or not in chapter 21. Instead, you will get Sylmeria and 10,000 Gold.