Do you see a problem with this swap?
 

I just ordered a set of 700x23 tires for my Gary Fisher and was talking with a friend of mine and he didn't know if it will fit. I am currently running a 700x32, and I know that is a big change and I'm o.k. with that. Just making sure. And being new at running skinny's is there any extra precautions I should take? Like rim tape etc. Will be doing road and greenway riding.

A 23mm road racing tire just needs clean roads to avoid punctures.
The speed difference of some 28c tires in comparison to 23's is hardily noticeable and can be got near puncture proof. I use 23's on some rides to.
Have a look at the internal rim width on your bike to run a 23 tire the width is recommended at 19mm but mine is 23mm and still works fine.