Two problems:

1. All dialogs were opening with the same data. This made all the close buttons only close the most recently opened dialog. Fixed this by adding the 'new' keyword before the call to $.ui.dialogInit

2. Closing a dialog only sets it to display:none. However, reopening the dialog actually creates a whole duplicate dialog, rather than unhiding the existing one. This is because the if statement that checked to see if the div on which we call .dialog() is already a dialog was checking for the wrong css class (due to the way the dialog is built, the original div gets the .ui-dialog-content class, not the .ui-dialog class.