Thank you all for the quick reply. I experimented a little bit more (before I saw your reply). 
 
1. Cutting the ring with all cylinders at once gave me the same undesired results. 
2. Cutting a solid cylinder (instead of a ring) with all cutting objects at once, same as above. 
3. It works when I cut the holes at midheight first and then the remaining holes close to the edges. 
 
I did not try the solution that Michael suggested, trimming the cutting objects at the center, so 
they don't overlap. I will try this, I am sure it works. Yes, Michael, now that you mention to scale 
things up before cutting, I remember this was mentioned before at the forum. 
 
Thanks again, learned something new today. 
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