How does non-homologous end joining (NHEJ) work?
Non-homologous end joining indeed induces errors in the affected sequence. But you have to keep in mind, that NHEJ is an emergency repair mechanism which involves a "repair or die" chance. If the chromosomal break is not repaired it is not unlikely that the cell will get into apoptosis, or, even worse, develops into a cancer cell. Introducing small errors is a relatively small price compared to this, although this can still disrupt genes or regulatory sequences. For the mechanism have a look onto the figure (from the first reference):



For further reading have a look onto the Wikipedia article on NHEJ and/or the following references:


The mechanism of human nonhomologous DNA end joining.
The mechanism of double-strand DNA break repair by the nonhomologous
DNA end-joining pathway.