Thanks again for the info, all who replied!
After thinking about it for awhile, it dawned on me that I did not know the way the AR/MP 15 functioned. I know how my AK's and PTR operate from front to rear.
One comment that struck a cord was trigger reset.
I went online, saw how the Sport cycled, and remembered something that happened. On one of the times I had no trigger I recalled feeling a slight "click" when I started to let off the trigger to clear the round. The gun then fired said round. Didn't think much about it.
The gun is "used" but the guy only had it for 3 weeks before he let it go. I figure he was having this problem but didn't tell anyone..
After the comments here, and a YouTube "How The AR 15 Trigger Works" I decided on the first course of action.
I removed the hammer and disconnect.
I didn't see any burrs, but the contact points were very sharp, and dry.
I lightly polished both surfaces with emery, then wet 1200 grit, then buffed out with Brasso. Lightly coated both surfaces with some of my precious "Swiss Grease" that I had for my K31.
Put it all back together this morning and went to the creek where I shoot.
Loaded up 10 rounds of Winchester 5.56, and clicked the safety to FIRE. APPREHENSIVELY squeezed the trigger, and it fired. Ran 3 more rounds with no problem. Was waiting for the "dead trigger" on the next shot. BUT! It fired! Went thru the 10 rounds with NO PROBLEM!!
Then, I proceeded to put 40 American Eagle .223 thru it. 40 more Win. 5.56, then, just for trial, 20 rds of TulAmmo steel cased .223.
NOT ONE HICCKUP!
As a new AR 15 platform owner, I am VERY pleased.
As I stated, an AR15 was not on my "must get" list ( I have AK's, a PTR, and a CETME...with plenty of ammo for both calibers) but the deal, and FUN I will have with this rifle has changed my mind. I may pick up another, when the Wife buys new shoes..