Not sure about the profile change.
You can know what objects you have access to (fully or partial if they are not created yet) with the objects linked in the blocking task object.
Typically the object on which you act but sometimes the one used to create it (i.e Template). The params section also contains some information.
One problem is that there is no access to all the information the end user has entered or in some case (Delete vApp) the object related to the blocking task is just a shelf without content.
Partial work arounds are to get information using the query service or information contained elsewhere (i.e Template).