Note: All credit for the finding of these glitches to the original people who found these glitches, if you are the person or know who the person is/was: Email me here.
1. Mine Glitch
This glitch involves placing a mine on the ground and when an enemy unit steps on that space, the damage animation should appear. Turn off the game. When you turn the game back on you should be able to control all the enemy units. This is a very useful glitch because you can make the enemies drop their weapons, move the enemies, Move the boss, and if the enemies are near Merlinus they you can make them put their weapons inside the merchant.
2. Ninis's Grace
Glitch involves using the Ninis's Grace Ring that Ninian/Nils have. First you use it on a unit and then send the unit into a battle/the arena. Once finished rescue that unit and end your turn. On the next turn drop the unit, the unit should still have the effect of the ring, Now use Ninian to dance for the unit so they can go back into the arena and fight. Rescue and repeat. This allows you to have the special Ninis's grace effect over and over again without using up the ring.
3. Uber Spear
In CH: 24(E)/26(H) the boss (Vaida - Wyvern) is apparently protected by Nergal's magic, but in fact it is the spear she is carrying that gives her the extra stats. Also notice that in the chapter there is a shaman who has a droppable Luna tome. If you use the Mine Glitch (above) you can make Vaida trade the "Uber Spear" for the Luna thereby making it so that when you kill the Shaman you get the Spear and when given to a unit they get all the bonuses.
Note: In Hector mode Vaida is in the opposite side of the map so she is much farther away from the Shaman. In this case it would take at least two mines to get her to the Shaman.
4. Dead Archer
In CH:5 (Lyn Mode) in the scripted battle between Erk and the archer, if Erk gets a critical hit he will kill the archer. But since the archer is supposed to be alive at the end of the battle, he will stay on the field with 0 HP. Attack it again to kill it.
5. Set's Litany
Pointless Glitch. If you use the ring Set's Litany on a unit and then while still on your turn you turn the game off, when you turn the game back on the effect will be gone.
6. Item's Return To Full Usage
If an enemy thief steals an item from you and you steal it back, the item will be at full usage no matter how many times you used it already.