The Undo button is available on the collection toolbar for all tabs. Click the button on press Ctrl+Z on the keyboard to undo the last change. Click the downward pointing arrow next to the Undo button to see the last 16 changes. If you click on an item in the list, that change and all changes above it (i.e. made after it) will be undone.
While the undo button only shows 16 changes at a time, AceText remembers all changes you've made since opening the clip collection. You can undo them all by issuing the undo command repeatedly. Use the Redo button if you change your mind about undoing something.
To keep the length of the undo history manageable, AceText consolidates editing actions affecting the same clip when you activate another clip. E.g. if you type three words at different spots into the text of a clip, those three actions will appear as separate actions into undo history, and you'll be able to undo them one by one. Once you switch to another clip, AceText will consolidate the three typing actions into a single "edit clip" action that will undo all three typing actions at once.
AceText keeps separate undo information for each tab. Clicking the Undo button will only undo changes made to the active tab. They will be undone independently of other tabs. Actions that affect multiple collections, like moving clips or search-and-replace across collections, have to be undone in both collections if you want to completely undo them. The advantage is that if you make changes in collection A, then make changes in collection B, you can undo some of the changes you made to A without having to undo anything in B.