Updates tonight:
Added labels for Edit/Save/Undo/Delete buttons on Bills and People lists. Thanks to Vy for the suggestion.
Added a "Click to add Bill/Person" note on Bills and People lists to make it more obvious how to add a new person. Thanks to Holden for the suggestion.
Major thanks to Kal-EL on EFnet #ASP.NET for the tip to set the LABEL text instead of CELL text. On re-draws, the blank label text was writing over the cell text and causing the "click to add" to disappear. I was baffled and spent hours trying to get past this. There were so many variables ... poorly formated CSS styles? Bug with AJAX? I tried everything before Kal-EL had a great suggestion to try setting Label text instead of Cell text.