Hi,
I normally don't look the stress results as nodal value. Most standard FE softwares provide average and non-average version of element result. Most of them are computed directly from Gauss points. As nagi said, the differece between average and non average results exhibits how accuracy the solution is. For theoretical converged solution, there should have no difference at all, since most elements are in constant state of stress.
Another hint is that if there is a high variation within a single element like some stress component change its sign (usually shear stress in beding dominated problem or normal stress in an incompressibility condition), make a refinement at that region or used enhanced strain element.
The result from that kind of mesh is usually lock in some way. This might be 200% or more different from the exact solution
Bests,