There is an increasing demand to investigate questions in observational studies. The propensity score is a popular confounding adjustment technique to ensure valid causal inference for observational studies. Observational data often have multilevel structure that would lead to one or more levels of confounding. Multilevel models are employed in Bayesian propensity score analysis to account for cluster and individual level confounding in the estimation of both the propensity score and in turn the exposure effect. In an extensive simulation study, several propensity score analaysis approches with varing degrees of complexity of multilevel modeling structures are examined in terms of average absolute bias and mean square error. The Bayesian propensity score analysis for multilevel data is further developed to accomodate misclassified binary responses. Errors in response can distort the exposure to response relationship. The true exposure-response surface can be recovered through two classification probabilities, the sensitivity and specificity. These link the observed misclassified response and the unobserved true response. Incorpating misclassification greatly reduces bias in exposure effect estimation and yields coverage rate of 95\% credible sets close to the nomial level. Strong ignorability is the fundamental assumption for propensity score. There is little literature that discusses this important but untestable assumption. Without the confidence that there are no unmeasured confounders, we assume the existence of unmeasured confounding and assess the sensitivity of exposure effect estimation to unmeasured confounding through two sensitivity parameters which characterize the associations of the unmeasured confounder with the exposure status and response variable. The influence of unmeasured confounding can be examined by possible change in exposure effect estimation with hypothetical values of sensitivity parameters.