Drupal 6.21-dev
Node Import module version 6.x-1.2
I was getting the above error in the log after trying to do an import and failing repeatedly. After some digging around it looks like the tables that get installed with this module, node_import_tasks and node_import_status, both have a field "file_offset", but the code is expecting the field name to be "offset".
At first I thought the mismatched tables were leftover from a previous version install but I completely uninstalled Node Import and verified both tables were gone, then installed it again and had the same mis-match.
SOLUTION: I added an 'offset' field to both tables and the import worked. If you're comfortable with MySQL you can do this:
mysql> alter table node_import_tasks ADD offset int(10);
mysql> alter table node_import_status ADD offset int(10);