Two-way fixed effects (TWFE) models are ubiquitous in causal panel analysis in political science. However, recent methodological discussions challenge their validity in the presence of heterogeneous treatment effects (HTE) and violations of the parallel trends assumption (PTA). This burgeoning literature has introduced multiple estimators and diagnostics, leading to confusion among empirical researchers on two fronts: the reliability of existing results based on TWFE models and the current best practices. To address these concerns, we examined, replicated, and reanalyzed 37 articles from three leading political science journals that employed observational panel data with binary treatments. Using six newly introduced HTE-robust estimators, along with diagnostics tests and uncertainty measures that are robust to PTA violations, we find that only a small minority of studies are highly robust. Although HTE-robust estimates tend to be broadly consistent with TWFE estimates, discrepancies in point estimates, increased measures of uncertainty, and potential PTA violations call into question many results that were already on the margins of statistical significance. We offer recommendations for improving practice in empirical research based on these findings.