Molecular testing helps give additional information about what genetic errors a thyroid cancer has acquired. Some of these errors are associated with more aggressive tumour behaviour, but quite how that helps make treatment decisions is still a bit unclear.
Here's a useful discussion involving some key leaders in the field (always worth listening to what Dr Tuttle has to say on thyroid cancer).
In the hospital I work in (in New Zealand) we have decided not to include molecular testing. Instead we are going to wait until we can be convinced that such testing will result in better patient outcomes before we add it to what we do. However, we'll be watching this space with keen interest in the hope that it will soon offer clear benefits to patient care.