Accuracy of Laplace Method for determining orbital elements
In principal, Laplace's method (and Gauss's method) should be very accurate for determining orbits. 

Of course "garbage in garbage out" applies, and if the observations were inaccurate the results may also be inaccurate. However, you should not get great discrepancies. I would consider careful checking of your calculation, and perhaps comparing your results with those of an independent orbital determiner, to check for a mistake in the maths.