We derive computationally simple expressions for score tests of misspecification in parametric dynamic factor models using frequency domain techniques. We interpret those diagnostics as time domain moment tests which assess whether certain autocovariances of the smoothed latent variables match their theoretical values under the null of correct model specification. We also reinterpret reduced-form residual tests as checking specific restrictions on structural parameters. Our Gaussian tests are robust to nonnormal, independent innovations. Monte Carlo exercises confirm the finite-sample reliability and power of our proposals. Finally, we illustrate their empirical usefulness in an application that constructs a US coincident indicator.