The main issue with DSGE models is that their simplifying assumptions make them useless for prediction: they replaced essentially atheoretical time-series models with hard, unrealistic theoretical assumptions about agent behaviour (over)fitted to time series and gained only a veneer of sophistication. Arguably no representative agent is better than a badly specified agent.
As an intellectual exercise to show that (for example) menu costs or nominal wage rigidities or technology shocks alone could have the economy's accounted for a shift from a [purely theoretical] equilibrium over a time period they're very interesting. For identifying which aspect contributed most towards economic change they offer little, and as a policymaking tool they're actually worse than useless since the models are generally built on the economists' assumptions about agents' response to policy and fitted to the data to justify those assumptions, rather than using the data to understand how responsive, rational and optimizing agents actually are. As such, their forecasting performance isn't very good either...
As an intellectual exercise to show that (for example) menu costs or nominal wage rigidities or technology shocks alone could have the economy's accounted for a shift from a [purely theoretical] equilibrium over a time period they're very interesting. For identifying which aspect contributed most towards economic change they offer little, and as a policymaking tool they're actually worse than useless since the models are generally built on the economists' assumptions about agents' response to policy and fitted to the data to justify those assumptions, rather than using the data to understand how responsive, rational and optimizing agents actually are. As such, their forecasting performance isn't very good either...