I have an older K80 (1999) it started missfiring once in maybe 100 then once in 50 or so. I took to Phillips gunsmithing and he had to replace some pins, that took care of it. It probably had close to 100,000 rounds though it before a gunsmith ever looked at it.
Look at your firing pin with a magnifying glass. it should look shiny and smooth. If it is chipped or not as described above it's bad. If you shoot Factory NEW shells other than GM-STS or AA you will have problems punching through the primers and burning the pins. If you reload using a Cheditte type primer will cause the same problem. WIN-FED-REM 209's will not give you problems.
Krieghoff has a free firing pin fix if you want to shoot anything other than Premium shells.
Don't take your gun anywhere. Primer problems happened with Estates and Top Guns in some of last year's batches. They'll make them good and I understand the problem was solved and all is well.
Federal and the other American ammo companies have all proven, to me at least, that they are all honorable and react to problems with the customers in mind. All companies have problems ..... It's how they react to them that separates the best from the also ran.
Cock gun. Break it down until you've got only the receiver and stock. Turn up and place EMPTY shell on breech face lower barrel standing up. Pull trigger. If empty shell rises several feet look elsewhere for problem. Do same thing with top barrel for comparison. Practice makes perfect. Now wasn't that easy!!
Are you using release triggers. If so, I've had the same problem and found that I'm not releasing my finger completely after the first shot and not holding the gun tight against my shoulder. This causes the recoil to let my finger pull the second trigger.