Hi there!
Bugs are tracked either in Ubuntu (which would be at
bugs.launchpad.net/ubuntu/+source/gnome-do/+bugs) or at github:
https://github.com/gnome-do/core/issues
I'm not aware of any particular problems with Xubuntu integration or
web search, but you can get more information by quitting Do and running
“gnome-do --debug” in a terminal to generate lots of debugging
information.
If you can reproduce the problems while running gnome-do --debug,
attaching the output of the terminal will likely be helpful.
Thanks,
Chris