I notice that in my program the MCMC of most parameters seem ok (the lines are close together, there isn’t much and the values seem to converge). The multivariate diagnostics also seem ok.

But some of the MCMC graphs for a few parameters do not seem to converge to the same value.

Since the multivariate diagnostics are ok, does that mean I can ignore the problems with those parameters?

I do not have many experience with Bayesian methods, I do not know how common should it be for us to not encounter problems in any parameter.