Is it possible to set the ID for the buttons in a jQuery UI dialog, so that I can refer to them later through jQuery? For example, trigger events, disable etc?
Not through the way you want as the API doesn't provide those options however if you look at the markup generated by the dialog box you should be able to grab whichever elements you need and bind them as you want or add ids to them. Here is the markup as found of the documentation page (http://jqueryui.com/demos/dialog/)
If it's buttons inside the content of the modal then you can do CSS queries in the modal element context and get access to them that way.