The refresh method is documented in the API but not implemented:
We need to implement this a bit differently for 1.4 vs. 1.3.x.
Closing as fixed by commit 922c562 (PR #5854)
On the demo page ( http://view.jquerymobile.com/1.3.1/dist/demos/examples/tables/columntoggle-refresh.html ), the last column (reviews) is not displayed again, if the window gets bigger.
The columns with data-priority 2 and 1 stay visible, no matter how small the window gets.
On my page, the columns in the tbody are now hidden correctly, but the th's stay visible.
This seems to be a problem with the "switchboard" - checkboxes. They are no indication if the user wants the th to be visible or not - because they are checked even when they haven't been touched.
However, this is only a problem on resizing, so maybe not top priority. In the meantime, for people having problems with that: if the switchboard is not important to you, comment out the self.update function (line 10913 - 10924 in jqm 1.3.1).
I checked my 1.4 table refresh code... it is lacking... I will try to fix right now and PR, so it will be early for me and late for you ;-)