Is there any way to catch the exception from UrlFetchApp.fetch?
I thought I can use response.getResponseCode() to check the response code, but I'm not able to, for e.g when there is 404 error, the script not continue and just stop at UrlFetchApp.fetch
Update: This parameter is now documented here.
Original answer
You can use the undocumented advanced option "muteHttpExceptions" to disable exceptions when a non-200 status code is returned, and then inspect the status code of the response. More information and an example is available on this issue.