No check constraints. Spotty transaction isolation. Silent data corruption if you happen to make certain kinds of updates while using statement-based replication. No on-line schema updates (is that still true?). Complete inability to execute joins of any size in reasonable time due to the lack of merge or hash join strategies. Corresponding inability to handle subqueries of any complexity. Readers block writers (at table level with MyISAM - and still at row level with InnoDB?).
As well as things like that which are actually ridiculous, there is also the substantial gap in features as compared to real databases. Things like recursive queries, user-defined types, partial indices, etc, are commonplace in the more sophisticated databases. You probably won't need them for a simple web application (or even a complex one!), but they can be very useful when trying to do more complex things, or manage a complex system efficiently.