I have a Colt MKIV Series 80 Officer's Model. When the hammer is pulled back to half-cocked, I can't put the safety on and I can pull the trigger and drop the hammer. This is the only Series 80 I have ever owned but I was told that if the pistol is half-cocked the trigger can't be pulled.

When full-cocked all works fine. When I carry this pistol I carry it full-cocked, but I just want other opinions regarding the function of this pistol when only half-cocked.  

The series '80s I have are just like that. The 1/2 cock is more like a shelf, positioning the hammer much closer to the slide so pulling the trigger supposedly drops the hammer gently. I changed one of mine over to the regular hammer with a 1/2 cock notch and it is just fine too. If you have any doubts about the series '80 system, put in a primed ONLY case and pull the trigger from that position, of course, still pointed in a safe direction.

Your Colt has an inertia firing pin. The firing pin is shorter than the distance needed to travel in order to fire the primer. The hammer dropping from the "half cock" shelf of the series 80 will not generate enough forward momentum for the firing pin to detonate a primer. Hope this makes you feel better