The only suggestion i can say that check your laws because any 1 m16 part in a non nfa gun can land you in hot water.It doesnt matter if the gun is semi auto or not.

You need to get rid of that bolt carrier, or have it modified to AR15 configuration.  ar15robert is correct- ATF has decided that if  you own an AR15 with ANY M16 parts in it, it's a machinegun even if it won't fire full auto.

You could just give it to me

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The M16 bolt carrier has a longer "bridge" that encloses the bottom of the bolt carrier.  This longer bridge section interacts with the Auto Sear which is needed for fully automatic fire.  The presence of the M16 bolt carrier should not affect the performance of an AR15 as long as the AR15 has standard parts.  The presence of the M16 bolt carrier can, however, earn you a fellony should your rifle ever be inspected by a knoledgable law enforcement officer.

If by cycling the next round you mean that when you fire a round with your semi-automatic rifle, the spent bullet casing is ejected, but the next round does not make it into the chamber properly, that sounds like an unrelated problem.  The presence of the "bridge" in the M16 bolt carrier shouldn't cause this.

I wouldn't worry about selling a part that doesn't function.  Just having that part around your house while you own an AR15 could be just enough evidence for some BATF agent to charge you with the intent to convert a gun into a machine gun.

If I were you, I would exchange that M16 bolt carrier ASAP, throw it away, or mangle it beyond any practical use.  Just buy a new bolt carrier.

www.bushmaster.com/shopping/uppers/8448505-s.asp

Personally, I prefer to use the M16 bolt carriers in my AR's...
All I do is grind back the sear contact area to match the AR15 carrier...
You can't "mill" it away because the metal is too hard...You have to grind it off with a grinder...
The reason I prefer the M-16 carrier is because it has a longer hammer ramp that shrouds the firing pin...

I've beat up too many firing pins with the unshrouded AR-15 carrier...
Seems the hump in the hammer is what contacts the firing pin as the bolt is closing, and it mashes the step on the front side of the hammer strike area...
Sometimes it even affects the reliability by hanging up on the hammer...

Just my 2-cents...