Lots of kids are just antsy and wiggly that way. It would be interesting to know if he does this at school and, if so, how the teacher handles it. Try using the same language at home as at school, which tells them it's a "universal rule" and not just Mom being a pain. Make sure Dad and babysitters use the same language too.
My reactions would be the following:
1) Stop commenting on it. I'm not sure that "Feet on the ground" is something you can enforce.
2) Remove books from the floor. If board games aren't being played, pick them up. "Since you're done playing and only want to step on it, we'll put it away." On some level, if it's his possession, it's his. If he ruins it, it's his loss. If you start with smaller things this way and a limited number of toys out at any one time, he'll see the loss of the toy/game more readily. He can also be involved in taking things to the trash can or the city dump and saying goodbye to them forever. The novelty of that will wear off soon.
3) Rungs of chairs: so, he'll fall and get hurt. He'll learn. Kids don't predict consequences (neither do teens, not very well). So sometimes they have to get hurt. As long as it's not life-threatening, it's not that big a deal. When my kid wanted to climb on the rock walls that are all over New England, I told my babysitter to just teach my son how to do it - how to test a rock first to see if it would wobble, and so on. They're going to do it anyway, so do your best to teach safety skills. Then let the bumps and bruises happen on a smaller scale long before the kid decides to climb on the neighbor's roof!
4) Breakables: put them away if they're yours. If they're his, let him break them, say, "Oh well, that's what happens when we step on things. Now it's gone. Poor you." And don't replace them.
5) Furniture: no shoes in the house, only clean socks and clean feet. See it as a positive - he's learning about his body, how far it extends, what things feel like with not just his hands but his feet as well.
6) If his feet are on other people, then leave the room or send him out until he can respect his personal space. If there's some furniture he can't do this on (like the good living room stuff vs. the playroom stuff), fine - have rules. "If you want to put your feet on the furniture, go to the X room which is the only room where this is allowed." That will help distinguish between what he can do at home (in some places) and what he cannot do at others' houses.
7) If bookshelves and dressers are not currently bolted to the wall, see that you take care of this. Too many kids are injured severely by tipping things over on themselves or on their siblings. Manufacturers make the right brackets, but hardware and baby supply stores also have things that adapt to other products.