The reconstruction of current sheet geometry is investigated as a function of paths through an oblique two-dimensional (2-D) hybrid supercritical shock and two fluid simulations of the magnetopause with no, small, and large guide fields, respectively. For world lines near the separator or 2-D structures in shocks, systematic errors swamp statistical ones tenfold. The systematic angular errors of the magnetopause surface normal determined by minimum variance analysis (MVA) using >100,000 world lines are contrasted with recommended statistical error cones. The systematic errors range as high as 90¿ but typically more than 20¿. Errors do not have a most probable value at the magnetopause when using MVA on the magnetic data, MnVA(B), and remain substantial when the Faraday residue, MnVA(FR), is minimized. The 68% confidence error on MnVA(FR) normals is 0--15¿. Skimming world lines oblique to the current sheet normal are the most susceptible to the MnVA(B) and MnVA(FR) systematic errors discussed here, whether or not the world line pierces the separator. MnVA(B) almost always erroneously insists that a guide field is present when none is present in the simulation. MnVA(FR) does a better job at guide field recovery, although it too can be error prone. Similar issues are demonstrated for oblique world lines through a 2-D hybrid simulation of an oblique supercritical shock. Shock normal systematic errors are 35¿ and 20¿ at the 68% confidence for MnVA(B) and MnVA(FR), respectively. The eigenvalue ratios that accompany the least error prone MnVA(FR) reconstructions usually satisfy λ2/λ1 > 10. Eigenvalue ratios for MVA(B) are rarely this large, and the errors reported here reflect this circumstance.