You have two questions to look at. One is chain adjustment, and the other is whether the chain needs to be replaced.
For slack, there is a specification of how much the chain can be moved up and down (sorry for the non-technical wording of that). On my 2007, it's 45mm-55mm from pulling the chain all the way up to all the way down. Check the manual for where to take the measurement. Mine either touches or is close to the swingarm even at proper adjustment, so don't be alarmed at that. Just check the measurement and tighten if necessary.
Before I replaced my chain, I noticed stiff links. The way I checked is that the links don't fully go parallel after going around the front sprocket. I put it on the centerstand and rotated the back wheel. As the chain came off the front sprocket, most of the links went parallel again, but some didn't. My chain had 30k miles or so, so I figured it was time to change it out. Here's a thread about how my chain looked before, as well as the change out procedure.
http://www.600riders.com/forum/fz6-technical/45813-chain-sprocket-change.html
That's the limit of my chain expertise/experience. Hopefully others can give more guidance if needed. Good luck!