I also run ozone through my skimmer. I believe that it is recommended to run the exiting water over activated carbon to break down any remaining ozone. I have read other opinions that the life of the ozone in water is so short that this is not necessary. Just to be safe, I do run my water over carbon. Additionally, you have to run the air coming out of the skimmer through charcoal. With the charcoal, there is no noticeable smell in my fish room. If I take the cover of the skimmer cup off, the smell is very noticeable.
As Aquaman said, ozone can degrade many plastics and rubbers/seals. So, if you choose to do this, buy a skimmer that is built for use with ozone.
As for the benefits of ozone, everybody has their own opinions. Mine is that a small amount of ozone goes a long way in clearing up water. All of the reports that I have seen of problems have been due to gross overdosing.
JD