great addon, but I think the release of this totally rewritten code probably has been done a little to fast. However, I also deal with this problems, also a multisite.
The issue in the github bugtracker brings me the solution to prevent the query.php errors. (https://github.com/jchristopher/attachments/issues/32) To my opinion there is no need, to search for old attachments 1.x and attachments pro meta fields in the constructor, because you want the plugin to be a tool for developers and they will migrate when updating.
As a quick workaround everybody who has not made use of attachments pro in the past can manually set this value in wordpress' database to prevent these query.php 1702 errors:
INSERT INTO wordpress.wp_options ( option_id, option_name, option_value, autoload )
VALUES ( NULL , 'attachments_pro_migrated', '1', 'no' )
If migration has not occured you can add this line after line 237 in class.migrate.attachments.php:
add_option( 'attachments_pro_migrated', true, '', 'no' );
For me this does work, I just comment here, because I hope this will help make it work for multisite out of the box in next version.