How to disable edit links/tasks for mobile theme?
Items should be disabled, if they are usually enabled, but not useful in that particular circumstance. For example, a submit button could be disabled when the form does not validate. Having an item that is permanently disabled raises the question why the item is displayed at all.

If you want to hide the items, you can do this using CSS if there is an appropriate CSS selector. Have a look at the HTML to figure that out.

For Drupal 4.7.x, 5.x and 6.x, you can also remove the links as described on the drupal.org page Remove unwanted tabs from pages.

Note that both methods only remove the link from the page. They do not prevent users from actually editing the page (e.g. by entering the URL manually).