1) The floppy disk icon displayed on the toolbar button does not actually reflect the sense of the Save Table operation. When working with database editors, you expect the Apply Changes button on the table's pane or the column changes in the table are applied automatically.
2) Turning off filtering is not really obvious as I couldn't find how to do it but to reopen the table. It's preferably to have the filter button to be able to turn it on/off and not to reset it when it's turned off.