The vast majority of tweets imported do not display their contents in the TT widget, the wp-admin->Posts (Excerpt View) or using the plugin/widget "Query Posts". A very small number do, but when reviewing the database entries in mysql, there are no settings differences between them whatsoever.
The tweet contents are stored in the db, and when viewing the tweet through wp-admin/Edit, the text shows up fine.
By pure chance, I happened to try displaying the tweets using the Query Posts plugin, which shows the Tweet titles, but not content. Then, when I disabled the Twitter Tools plugin, the content correctly shows up for all the tweets! Obviously this is not a permanent solution - has anyone experienced this and know the cause/solution?