Multiword expression (MWE) identification has been the focus of numerous research papers, especially in the context of the DiMSUM and PARSEME Shared Tasks (STs). This survey analyses 40 MWE identification papers with experiments on data from these STs. We look at corpus selection, pre- and post-processing, MWE encoding, evaluation metrics, statistical significance, and error analyses. We find that these aspects are usually considered minor and/or omitted in the literature. However, they may considerably impact the results and the conclusions drawn from them. Therefore, we advocate for more systematic descriptions of experimental conditions to reduce the risk of misleading conclusions drawn from poorly designed experimental setup.