Once you have dumped the tree you can save it and then use some distance calculation against the new dump. For example:
# dump the tree
tree1 = vc.dump()
# do something, here, like touch to navigate
someView.touch()
# dump again
tree2 = vc.dump()
# calculate the distance
d = distance(tree1, tree2)
Obviously, the trick is in how to select the distance method. You can convert the trees to strings and then calculate the Hamming distance if they are the same length, or Levenshtein distance if they are not.
I have been using this method on some projects. The only thing you should consider to apply the later is the size of the strings, as the matrices become very big. Future versions of AndroidViewClient will include some of these facilities.
Alternatively, you can do some visual comparison as described here.