This paper is concerned with various issues related to inference in large dynamic panel data models (where both n and T increase without bound) in the presence of, possibly, strong cross-sectional dependence. Our first aim is to provide a Central Limit Theorem for estimators of the slope parameters of the model under mild conditions. To that end, we extend and modify existing results available in the literature. Our second aim is to study two, although similar, tests for breaks/homogeneity in the time dimension. The first test is based on the CUSUM principle; whereas the second test is based on a Hausman-Durbin-Wu approach. Some of the key features of the tests are that they have nontrivial power when the number of individuals, for which the slope parameters may differ, is a “negligible” fraction or when the break happens to be towards the end of the sample. Due to the fact that the asymptotic distribution of the tests may not provide a good approximation for their finite sample distribution, we describe a simple bootstrap algorithm to obtain (asymptotic) valid critical values for our statistics. An important and surprising feature of the bootstrap is that there is no need to know the underlying model of the cross-sectional dependence, and hence the bootstrap does not require to select any bandwidth parameter for its implementation, as is the case with moving block bootstrap methods which may not be valid with cross-sectional dependence and may depend on the particular ordering of the individuals. Finally, we present a Monte-Carlo simulation analysis to shed some light on the small sample behaviour of the tests and their bootstrap analogues.