I have a bolt action rifle that is drilled and tapped for iron sights.  The holes that were drilled (done at the factory) are on the barrel.  I took the Iron sights off years ago.  The rear holes that are drilled are missing their screws.  No clue what has happened to them.  These holes are 1/2 an inch or so after the chamber on the barrel.  Obviously the holes don't go down through the barrel.  Is there any issue shooting the gun without the screws in the drilled iron sight holes?

What kind of rifle and what is it chambered for?

I'd be foolish to tell you it's perfectly safe, and that millions of barrels are drilled and tapped for irons, and that I've never heard of a barrel bursting due to sight holes drilled into it. Or that having the screws in it would have little effect on strength anyway.

I suppose if the holes were drilled to within a micron of the bore wall, a high-pressure load could conceivably finish "drilling" the hole.
Take  all of that for whatever you think it's worth...

Edited to remove quote tree. (Seeing as I was the first responder, it seemed rather unnecessary! )  

Yeah.
Brownells carries specialty "filler" screws for such applications.
They have a very tiny head so they cap off a hole neatly, and a slight crown to blend in on a barrel or receiver profile.
I think they're available in 6-48 and 8-32 sizes, and blue or stainless.