It is not easy to see small errors, but it is simple to see when things are going way out of wack. Just look for highly unphysical behaviour like rapid fluctuations of level without due cause. What can one do then? Find the time step size where major unphysical things are happening, then decrease it by a factor of ten. Either that or move to a better way of solving the differential equations. However, no matter which numerical method your choose, the time step problem still exists, so the above advice is still quite practical.