A comparison really requires comparing the environments in some way. I would create a database link on your test system to your live system and then do some simple data dictionary comparisons on user_tables and user_tab_columns. Any differences you find should be brought to the attention of the DBA so he can determine which of the following applies.
- The structure wasn't properly backed up.
- The structure wasn't properly restored.
- The structure was changed after the backup.
Having the specific differences from the queries will help him track the problem down.
Since you have concerns about missing tables and columns, I'd address that first and then you can look into comparing the content, see Compare content of databases in Oracle.