Non-relativistic theory is not good enough to accurately describe properties of a system. (Schrodinger equation is however a very good approximation in most cases.) Relativistic effects scale with nuclear charge (Z), that means that those effects are more prominent in heavier elements or molecules containing heavy atoms. Thus one should consider the relativistic effects to calculate properties of heavier system. Those effects are usually negligible for lighter elements.
If relativistic effects in the calculation of heavier system are neglected, quantitatively and/or qualitatively incorrect results may be obtained.
I totally agree with Kaushik Talukdar. To add an answer more, I advise you to read the very good book : Relativistic quantum chemistry by Kenneth G. Dyall. Some chapters highlight the importance of taking in account the relativistic effects in understanding properties of peculiar molecules bearing heavy elements. If you're interested in a PDF version of this book, I will be pleased to send you a copy of this latter.