With Drupal 5.0 and beyond, it is now possible to provide independent sorting of tables when they appear on the same page.

This is accomplished by inserting a unique label for each table in both the tablesort_sql and theme('table'... calls for each relevant table.

For example, suppose you had two sortable tables on a page, one a list of users, and the other a list of nodes. To make each table sortable independently, you would do something like:

For the user table:
...

$user_sort = tablesort_sql($header, NULL, 'user');

...and then in the user table theme call...

$output = theme('table', $header, $rows, array('class' => 'some-class'), NULL, 'user');

For the node table:
...

$node_sort = tablesort_sql($header, NULL, 'node');

...and then in the node table theme call...

$output = theme('table', $header, $rows, array('class' => 'some-class'), NULL, 'node');

Note that for each table, the label you use for tablesort_sql and theme('table'... must be identical for the independent sorting to be handled properly.