Mike Jordan wrote a report on his interesting survey on 50 statisticians by asking them what are the open problems in Bayesian statistics. Here is his report: http://members.bayesian.org/sites/default/files/fm/bulletins/1103.pdf
The top open problems in his report are as follows:
No.1. Model selection and hypothesis testing.
No.2. Computation and statistics.
No.3. Bayesian/frequentist relationships
No.5. Nonparametrics and semiparametrics
Andew Gelman made excellent comments on these problems. Here is the link: http://statisticsforum.wordpress.com/2011/04/28/what-are-the-open-problems-in-bayesian-statistics/