If you are using this with PHP the or die(mysql_error) part after the query is executed should inform you of any error that is occurring during the update.
If you would like to have a custom confirmation of the update you can do something like this:
Store the record id for the record you are updating in a session variable. Then on the page then user goes to next you can create a recordset to select the records from that table where the id matches your session variable value. When the record is found you can display the details of the current record to the user so that they can confirm that the update took place.
Making an update to a record using the DataAssist pages should take you to the detail page which will do just as I described above and allow you to view the values for the current record. This is the best form of confirmation that the changes made are taking effect. There are some other ways you can do this too. One alternate way that would be much more custom and is not a supported feature would be to store the existing values of the record in session variables, then after the update is submitted you can do a comparison of the new values against the old values in the session variables. So long as one of the values is different then the update occurred successfully. Like I said this is much more custom and is not a supported feature but it is just another idea of how you could do something like this.