So based on the newschoolers community, when ever a question comes up in the forms asking about "Should I remount my skis?" or "Is remounting a ski a bad thing?", the most common response you see is "ITS GONNA MAKE EM BREAK!" or some form of that. Based on my philosophy, I personally believe that it is ok to remount skis, so long as you have a shop that you are sure knows how to correctly complete the task. This would mean that you are positive they will fill the old holes with some sort of strong epoxy and that (to be very sure the skis are fine) they will fill the old holes with hole plugs or rubber pegs. This being said, I would go to your shop owner and have him remount your skis while you are standing right there if possible. This is what I did and I was 100% sure he put the epoxy in the old holes along with the rubber pegs. I feel that if the shop will not fill your old holes with epoxy, THEN it is not worth remounting your skis.
Another quick suggestion is when you are remounting, get some tape and label on your skis EXACTLY where you want them mounted for sure. By doing this, there is no way for the people mounting your skis to screw up. This would mean, taking a tape-measurement of the skis and marking precisely where you want the skis mounted.
Note: This is just my idea of the concept. I know that many may disagree but now I feel strongly about this. Leave comments or any feelings below. Thanks guys.