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Dynare should give warnings when priors are unbounded
It is generally a bad idea to have a prior with unbounded density, as even with reasonably tight identification, such a prior can easily swamp the likelihood. This is particularly problematic when the prior is unbounded at the edges of its support, as then the mode will be driven to the edge, causing further problems with Hessian computation.
At present in Dynare, it is a bit too easy to inadvertently specify such a prior, given the mean and std. dev. specification of the beta distribution. I would suggest that Dynare should give a warning when such are encountered.
For the beta distribution, the prior has bounded support providing alpha>=1 and beta>=1. This means that the variance of the prior must be less or equal to min(m*(1-m)^2/(1+1-m), (1-m)*m^2/(1+m)), where m is the mean of the distribution.