Reliable measures of poverty are an essential statistical tool to evaluate public policies aimed at reducing poverty. In this paper we consider the reliability of income poverty measures based on survey data which are typically plagued by measurement error and missing data problems. Neglecting these problems can bias the estimated poverty rates. We show how to derive upper and lower bounds for the population poverty rate using only the sample evidence and an upper limit on the probability of misclassifying people into poor and non-poor. By using the European Community Household Panel, we compute bounds for the poverty rate in eleven European countries and study the sensitivity of poverty comparisons across countries to measurement errors and missing data problems.