You need to look for the <div class="postmetadata"> in index.php, archive.php, search.php and single.php. Where you see <?php the_date(); ?>; write <?php the_modified_date(); ?>; instead. Let me know if it works! Check all the kinds of pages and archives where you would normally see the published date.
look for the functions.php file in your theme folder, you need to make the change in function twentyten_posted_on() as alchymyth said, there should be get_the_date() you can change to get_the_modified_date()
It can work without [end_columns], but when I used two rows of three columns it didn’t work in IE: the 4 columns were lined in the same row.
I was about to begin experimenting with CSS but I found that to make [end_columns] invisible, you can just use the span tag:
<span>[end_columns]</span>
