This study examines the behaviour of continuous time integration schemes over discontinuities in the tangential forces typical in an oblique impact within a Discrete Element Simulation (DEM). High order schemes are associated low error and efficient computation, however, for DEM this is not always the case. The simulations consist of a particle impacting tangentially with a plane and sliding along it, this makes the numerical integration independent of errors from the normal force integration. Three possible force regimes that occur in the tangential motion of an oblique impact are explored; frictional, elastic and elastic-to-frictional. Tests are conducted to explore the effects of the location of the discontinuity within the time step and to examine scheme order through varying time step resolution. For certain scenarios the tangential motion contains elastic and then frictional forces, this presents a second discontinuity between these force regimes. The effects of this second discontinuity are also presented. It was found that all schemes were limited to 1st order by at least one of the conditions tested. The Symplectic Euler is recommended as it is found to be of generally higher accuracy than other 1st order schemes in these tests, as was found in a similar study regarding normal impacts