As of MySQL 5.5 the default storage engine is InnoDB, which doesn't support fulltext tables. The HL Twitter installer tries to create 3 tables, but doesn't check the results and thus doesn't realize the table creation failed. Same problem with all the table queries, so it never knows the selects and/or inserts fail.
1. For MySQL sites, add "Engine=MyISAM" to the end of the create table statement.
2. Check the create table statement results to ensure that the tables actually get created.