1) Very limited ALTER TABLE support. 2) Very limited JOIN support. 3) No real multiuser/multiprocess concurrency support. Limited concurrency in-process with WAL. 4) Poor query optimizers, compared to PostgresSQL and even MySQL. Poor index analysis in complex queries.
4 is really a big one. It's surprisingly easy to hit situations where SQLite is orders of magnitude slower than real databases, fails to make proper use of available indexes to narrow range queries, does terabytes more write traffic than was necessary, etc. And unlike MySQL/PostgresSQL, the query planner inspection tools are horrible, too.
On top of that, some SQLite features (R-tree, slightly less bad index analysis, ...) must be enabled and aren't compiled in by default. This complicates deployment.