In robotic needle steering, adverse events such as needle buckling, undesired curvature changes, and tissue displacement can occur during needle insertions into tissue, preventing accurate needle placement. This paper focuses on detecting tissue displacement and needle curvature changes using data-driven detection algorithms, informed solely by needle and tissue position measurements. The algorithms were evaluated for different needle insertion velocities and duty-cycles, and analyzed using a Kruskal-Wallis statistical test. Results show that with increased insertion velocity, tissues displace sooner (p <0.01), while duty-cycles have no effect. Furthermore, with increased insertion velocity and lower duty-cycles, the needle curvature radius decreases (p <0.01). Additionally, the algorithms were evaluated for needle insertions into ex vivo liver tissue, under live fluoroscopic imaging. The goal of this study was to evaluate the effects of constrained or unconstrained boundary conditions on adverse events. As expected, unconstrained tissue experienced more displacement events. Fluoroscopic videos confirmed accurate and timely prediction of the adverse events. Finally, these algorithms were designed to detect multiple adverse events, simultaneously, and can be implemented in real time.