Missed home plate leaving the field
 

OBR - wild pitch runner trying to score jumps over glove? I guess anyhow appears to miss home plate as no safe (or out) call is made. Runner believing he has scored goes to the dugout and nothing happens. How is it any different than say a non-caught 3rd where maybe both sides believe it was caught and defense starts throwing the ball around and batter/runner goes into dugout.

We had the pitcher step off, throw home, catcher stepped on home, umpire called him out. But my question is if he missed home and went to dugout, wouldnt he be automatically out? I guess either he touches home or he doesnt and if he doesnt, whether the defense appealed or not, shouldnt he of been called out?

A missed base is assumed to have been touch unless appealed. Same at every base.

If there had not been an appeal the run scored.

In either case--uncaught 3rd strike or the missing of home plate--the runner cannot come out of the dugout to fix the problem.
Yes, if a runner who scored came out of the dugout to retouch plate I woulld not stop him but this would not negate the defense's ability to appeal.
As Rich has already stated a missed base must be properly appealed for the out to be recorded---as your pitcher did

Thanks guys, great info.