At the moment, the only thing I'm aware of is the Last Message column under services/requests. These will contain information from things like the On Entry, On Exit, and On Error fields in the state machine. For example, in the Provision VM from Template state machine, the update_provision_status method is run in each case with the appropriate status string in each field. This updates the Last Message field in the request status. These messages can be customized in the state machine.
Unfortunately they do not auto-refresh, so it will require you to manually refresh using the button in the top left if you want to follow the process closely from the UI. For debugging, tailing the log tends to be much more useful.