The maximum likelihood estimate that is not normal

For most models the maximum likelihood estimator is asymptotically normal with variance set by the Fisher information. But consider i.i.d. observations $X_1, \dots, X_n$ from Uniform$(0, \theta)$, where the maximum likelihood estimator is the sample maximum $\hat\theta = X_{(n)}$.

Show that $\hat\theta$ is not asymptotically normal, find its convergence rate and limiting distribution, and explain why the usual theory fails.