Monte Carlo Simulation…?

I just have 2 questions:

(1) If we can obtain samples from the posterior distribution, is there any need to try to compute posterior expectations and intervals analytically...?

(2) Also, I know that Monte Carlo methods will, in general, produce different results every time they are run, but how might I convince someone that my results obtained using MC are reliable?

Any help would be appreciated.

2) If you produce multiple MC runs - you can compare results. If your MC sample can guarantee independent samples, then a simple variance estimator ($\frac{\widehat{\sigma}^2}{n}$ type) can give you some idea of how good your expectation estimate is. If your MC sample is from a MCMC algorithm, say, Metropolis Hastings, some more careful thought and good diagnostics are required - typically looking at the trace plots and autocorrelation plots. I'm sure someone else can contribute much more to this discussion...