It's really clear to me in reading these comments that people posting haven't been downtown on a regular basis since the dog ban.  I live downtown(in the core) and it has changed dramatically.  Much more police presence, far fewer loiterers, very few dogs, the yelling and screaming has decreased markedly, the park blocks are cleaner and in general there is a happier attitude of those who visit/live here.  The issue of safety is improved through the increased police/red hats presence.  I don't feel like I'm walking on red alert like I used to.
Again, I live in the core of downtown Eugene where all the problems were occurring.  It's a much different place.  There will always be the mentally ill and street people/travelers who have trouble obeying the law but their numbers have decreased markedly.  I would encourage people to visit downtown and ask the business owners how they feel about the changes.  Every one of them I've spoken to appreciate everything that's being done.