Finite-element analysis is only as good as its inputs. A colourful stress plot can be confidently wrong — these are the traps that produce numbers you shouldn't trust.
Boundary conditions dominate
The single biggest error source. Over-constraining (fully fixing a face that's really bolted, or grounding a part that can actually lift) creates artificial stiffness and phantom stresses; under-constraining lets the model fly apart. Loads and restraints should match how the part is really held and pushed — not what's convenient.
Stress singularities
At a sharp re-entrant corner or a point load, the theoretical stress is infinite, so it keeps rising as you refine the mesh — that number is meaningless, not a real hotspot. Add the real fillet radius, or read stress a little away from the singular point. If refining the mesh makes a peak stress converge, it's real; if it keeps climbing, it's a singularity.
You refine the mesh at a sharp re-entrant corner and the peak stress goes up. You refine again and it goes up further. What does that tell you?
A sharp re-entrant corner has no finite stress in elasticity theory. Williams' solution gives σ ~ r−0.46 at a 90° notch, so the peak rises without bound as the elements shrink: whatever number you report is a statement about your mesh, not about your part. Real parts have a radius, real materials yield, and the fix is to model one or the other — or to stop reading the peak and use a method that does not depend on it. The test is convergence: refine twice. A feature with a radius settles; a singularity keeps climbing, and it climbs at a rate you can predict.
Try it — one of these converges and one does not
Mesh and elements
Do a mesh-convergence check: refine until the result stops changing. One element through the thickness of a bending part is too coarse. Prefer second-order (quadratic) elements; avoid highly distorted or sliver elements. Coarse mesh under-predicts stress.
Sanity-check everything
Before trusting FEA, estimate the answer by hand — a beam, a section stress, a deflection (the beam and section tools help). If FEA and hand calc disagree by an order of magnitude, the model is wrong, not reality. Check reaction forces sum to the applied load, deflected shape looks physical, and units and material properties are right. Linear-static also assumes small deflection and no yielding — know when those assumptions break.