a) shoes on table
Western Europeans also find the gesture of shoes on chairs and tables repulsive, both in public and in private.
In my experience, shoes on the table in public seems to be a US specific behavior, but please correct me if I'm wrong. You know, something you'd see in a Western. It's a very laissez faire gesture, of a confident and free people, unlike the stuck up Europeans with all their rules.
The most memorable experience for me was with the CEO of a company where I worked. He would do this in every meeting, even when we met with executives of another company. It could have been a dominance gesture, but more likely his hippy attitude.
I've also observed that people in the US tend to put their shoes where others will sit or put their hands, e.g. chairs, benches etc.
b) dog poo
People in the US pick up after their dogs, I find this great! A lot of Europeans don't, which is super nasty. The memory of dogshit in Paris and Berlin, especially on a hot summer day, makes me want to puke. Google for Paris and dogshit and see what I mean.
a + b) what it means
Now, to each their own, but from a hygiene/medical standpoint, shoes on chairs and tables should not be done. Let me explain why.
Even with no visible dogshit under your shoe, there are myriad diseases that can be transferred this way. It does not have to be as horrible as http://en.wikipedia.org/wiki/Echinococcus_multilocularis, but there are many others. Eggs of parasitic worms hosted by domestic animals are quite hardy. That's why I'd say, leave you shoes (not necessarily feet) of chairs and tables. Why risk infecting yourself and others? Like wearing a seatbelt, a simple behavior that can save your life.