Just found something that is set wrong.
While uploading and then adding an image to a post that is linked with its full size file, tags <img> receive "title" parameters instead of ! This means tags don't have any titles (title="sample_title") then!
<a href="link-to-a-file/image.jpg"><img title="description" class="alignleft size-thumbnail wp-image-57" src="link-to-a-file/image.-70x70.jpg" alt="" width="70" height="70" /></a>
THIS IS SORT OF WRONG - it is not search engines friendly... tags should receive title parameters set while adding pictures via the "add media/add images" module...
Adding images to a post should create a code like this:
<a href="link-to-a-file/image.jpg" title="description"><img class="alignleft size-thumbnail wp-image-57" src="link-to-a-file/image-70x70.jpg" alt="" width="70" height="70" /></a>
Moreover, you got used to insert lightboxed images via plugins (ad-lightbox and such), you're doomed - if you try to add new images into a post, there will be no more descriptions in lightbox windows for images anymore!
Hope it will get fixed with a new release of WP...