Twitter Tools is defacto Twitter-WordPress integration software, but it has one glitch that is easy to fix: tweet posts are formatted so horribly, it’s criminal.
By default Twitter Tools places the full text of a Tweet in post_content, and an abbreviated, ugly version of the tweet in post_title. This is fine, because there are (usually, depending on your theme) formats for the proper display of a status.
Open twitter-tools.php. After line 515, which reads
add_post_meta($post_id, 'aktt_twitter_id', $tweet->tw_id, true);
type a new line that reads
Next time Twitter Tools fetches tweets, it will format them as statuses.