Crack propagation calculations are often associated with the eXtended Finite Element Method (X-FEM) because it facilitates the calculation by eliminating the tedious remeshing process[1]. Level Set Method (LSM) is commonly coupled with X-FEM because it provides an efficient way to define and track crack geometries, even in three dimensions. With the LSM, a crack is represented by a pair of level sets functions which must satisfy the signed distance function and orthogonality properties. An accurate description of the crack and so the pair of level sets, is one of the key points for accurate X-FEM results. A first contradiction arises when these properties are in contradiction for complex crack geometries and cannot be simultaneously satisfied throughout the entire domain. Then, what constitutes an accurate description when all requirements cannot be met for a complex crack shape? When dealing with complex crack geometries, different methods allow one to define and to update the level sets but will never reach the zero-error point because it is simply impossible. Some methods will minimize the signed distance error at the cost of the orthogonality error, or the opposite. The aim of this article is to study the impact of the level sets errors on the X-FEM results. The article is innovative in its approach: rather than focusing on the level set errors, it studies their impact on the X-FEM results and how to minimize the resulting X-FEM errors. Different famous test cases ([2], [3]) will illustrate that the residual level sets error for complex crack shape is not to be neglected and may lead to significant inaccuracies on the fracture mechanics results. The study will show that optimizing orthogonality at the cost of the gradient norm leads to more accurate values of G and Stress Intensity Factor.