This thread is resolved. Here is a description of the problem and solution.
Problem: I'm having the "There is a problem with the String Translation table in your site." problem Solution: I went to the troubleshooting page and the "reset language tables" was there, which means that there was an issue over there. I pressed that button and then I checked the icl_strings table and it was working correctly. I repaired all tables just as a precaution and everything was fine. I then went to delete the "wpml_string_table_ok_for_mo_import".
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