It depends on the problem being solved and the element formulation.
The orthogonality criterion you state may not be as important as the shape of each element.
For example in structural mechanics, with an irregular (e.g. automatically generated and refined) mesh and isoparametric elements, an important criterion for accuracy is the largest angle between ...
Yes. The constants that appear in the interpolation estimates upon which finite element error estimates are based contain minimum and maximum angles of triangles/tetrahedra (or similar geometric measures for quadrilaterals/hexahedra). These constants are smallest whenever you have equilateral triangles or square quadrilaterals.