Bell tests have become a powerful tool for checking security, quantifying randomness, detecting entanglement, and many other applications, as well as for investigating fundamental physical limits. Most Bell experiments make the assumptions of fair sampling and equal detection efficiency, and some also the assumption of setting reproducibility. Here, we point out that there are typical experimental imperfections and practices that lead to the violation of these assumptions and can go unnoticed. This is a problem that can invalidate the conclusions of many past and future Bell experiments and allow for malicious attacks. Detecting, quantifying, and fixing this problem is therefore of fundamental importance, especially for modern applications where the experimental values are used to reach quantitative conclusions about security, randomness, or entanglement. To illustrate the issue and its causes, we present a set of Bell experiments using polarization-entangled photons, where we identify common imperfections and practices that cause the failure of the assumptions. These experiments tell us which methods we should avoid and to which aspects of the setup we should pay special attention. We show that the failure of these assumptions results in a violation of a fundamental requirement in any Bell experiment, namely, non-signalling. We present a test based on the deviation from the non-signalling conditions that quantify and help us to fix the problem. We emphasize that adopting the measures and conducting the tests suggested here is necessary in order to obtain reliable conclusions in modern quantum information applications based on Bell tests.