The forward assist on my Colt 6520 rotates about 20 degrees (more than the FA rotation on my 6920) and when pushed in actually misses the cut outs in the bolt, and consequently, does not shut the bolt all the way forward when actuated some of the time. Is this normal? Is there a way I can reduce the rotation play in the FA?

Thanks

The FA is held in proper position in the upper by a roll pin.  Perhaps that pin has somehow become bent.  I would take it apart, and troubleshoot the problem.  Instructions are in the TM -23.

No, it's not normal. I am guessing there is some wear or broken part, either the upper or the plunger, that is allowing the forward assist to rotate. Drive out the roll pin that holds it together, remove the spring, and figure out where the problem lies. If you have another forward assist to compare it to, that would probably make it even easier.
Generally speaking though, you almost never should touch your forward assist. If your bolt isn't shutting when you hit the bolt catch, then it's time for a new recoil spring. I can think of two applications of the forward assist. One, on military rifles that tend to see a lot of wear, recoil springs may not be replaced as often as they're supposed to. The forward assist is just a way of making sure that the bolt is fully seated in the carrier. The other is when you want to quietly chamber a round or chamber check, and  your bolt doesn't rotate and seat into place (not all that uncommon with new guns). Otherwise for day-to-day range use, it should be of the less-used features on the AR.

Thanks.  Can the ar-15 fire out of battery when the bolt is not fully closed?  

Quoted: Can the ar-15 fire out of battery when the bolt is not fully closed?

Nope,  not normally.  The firing pin will not protrude through the face of the bolt, unless the bolt is in the locked (fully recessed into the carrier) position.  Now if the cam pin were to break, or if you forgot to install it, then the bolt could be pushed back into the carrier without rotating to the locked position.  Thus you could fire the rifle without the bolt being locked.  That of course,  would cause some BIG problems.