I have a CBR f4. but I'm posting about another new ride I obtained.
For two reasons. Because it seems like a universal type situation.
Ad because this is one of the easiest motorcycle forums to navigate.
Just bought a 2007 ZZR600, and it's been doing great.
17k miles, all routine maintenance up to date.

I just noticed a problem for the first time today.
I went to make a U-Turn, and sometime between
the point I started turning, and started accelerating,
I got a real quick knock. It sounded/felt like it was right in front of me.
And maybe I'm just paranoid,
but now it seems like it's doing it every time I make
a slight turn at low speeds, and get ready to accelerate.
Like doing a rolling stop at a stop sign, turning a slight bit
to the left, and get on the gas again, it's a quick but distinct knock.

I'm hoping it isn't too serious cuz it don't seem to effect the power of my bike. though now I feel like my 0-60 isn't as good, but again, paranoid. :C

Hopefully someone can help me.

 

Do you know when the last time the chain and sprockets were done? The front sprocket on my old f3 got a little wallowed out on the shaft after a little while and exhibited roughly the same things you are concerned about. Pull the front sprocket cover off and pull the chain and see if you can wiggle the sprocket