With most boats, a centerboard will wobble side to side if there's no lift on it. Eg. you are going slowly, and the board is not resisting your leeway. Otherwise, when going faster to windward, the board will get pushed sideways and essentially get "pinned" to the side of the trunk.
As for vibration, this is common as well. Most boards are made with a bit of radius to the corners of the edges. I know this is true for my 2 fiberglass boards. This is because the fiberglass can't be molded with hard edges. So, as the water flows over the board, it can adhere to those slight radii, and get sucked around sideways at the back of the board, shedding little vortices alternating each side, and inducing a vibration. Racing boats will fill and fair the trailing edge of the foil, and square off the trailing edge maybe 1/8" thickness with 90º corners. This allows the water to flow straight off the sides of the foil, with minimal turbulence.
You can see this effect using a spoon and a piece of wood with square edges. Go to the kitchen sink, and run the water with a smooth column flowing out of the faucet. Lay the back side of the spoon alongside the water. The spoon will suck into the water, and deflect the water towards the front of the spoon. Now, take the piece of wood with square corners, and do the same. The water will flow cleanly down the wood, and flow straight off the corner. It won't suck the wood into the flow, nor will it deflect the water towards the corner of the wood.
I get the same vibration on my Harpoon with centerboard. I know that the trailing edges of the centerboard and rudder are rounded over. Since it's not a racing boat, and there's no racing class, it's not something I've addressed. I kinda want to, but it's probably not going to make me all that much faster, considering I have no gasket on the centerboard trunk slot to prevent water sloshing up inside and causing turbulence… and I don't race it much. Still, since my motto is "sail it like you stole it" it gets me to thinking I should fair the trailing edge and figure a way to glue on a gasket. Naaaaah, not worth the trouble…
My O'day 192 vibrates for a different reason, because the centerboard lifting pendant trails the board when it is down, and that vibrates as well… same reason, it's a round line making drag vortices...