We were there in May and stopped at Camping Fusina which was good. Huge container ships passing within a few feet of your MH not something you see every day. A short walk to the water bus. The multiday pass is well worth it if used. We were parked next to another Brit that had a dog and they had only spent 2hrs in Venice because they didn't think it suitable for the dog. Whilst there, there were quite a few locals with dogs but they would be brought up there and used to the hoards of tourists and traveling by boat which is anything but smooth at times. There are very few green spaces on Venice. As far as access to places with dogs I do not know. Personally I don't think its a place to take a dog. The amount if tourists is huge but if you want to see these places it something that has to be put up with.
I suspect any we saw without muzzles on were locals.
Taken from
Boat Transportation Venice ACTV Water Bus Vaporetto
Pets on board of Water Bus Vaporetto
You can go on board of the Water Bus Vaporetto with your dog if kept on a leash and muzzled.
Cats, birds and other little animals can be taken on board if inside a portable cage closed with maximum size of 120 cm (height + width + depth).
Paying an extra charge, you can use a cage of maximum size 150 cm (height + width + depth).
Beware that the captain can refuse to let you go on board with your pet, for instance, at the rush hour.