State of the art in DSGE modeling

I am not entirely sure which direction this is supposed to go. In its generality your question is impossible to answer. DSGE is an extremely large model class that covers pretty much all of non-deterministic macro models. The state of the art will differ depending on which subject you are investigating. Monetary policy models for example differ from structural change or social security models.

As you refer to Calvo and Rotemberg you seem to be interested in monetary policy models. Here, state of the art may be Heterogenous Agent New Keynesian (HANK) Models, which are currently one of the most active areas of research. They have the big advantage of allowing to investigate heterogeneity, while maintaining the core of elements that central banks are interested in.

The connection between time series econometrics and DSGE models has been discussed at