At what point do we start to trust scientific opinion?

I have spent quite a bit of time recently trying to sort out the difference between demonstrable scientific fact and informed scientific opinion.  An example of the former is the measurement of 'g', the acceleration due to gravity; the latter might be the opinion of medical practitioners and nutritionists that consumption of large amounts of saturated fat can lead to heart disease.  Few people would argue about 'g', but there is much discussion, even amongst the experts, about the effects of saturated fat in the diet.  An opinion gains validity when, if challenged, it can be supported by peer-reviewed research.

Of course, it is impossible to prove a negative, but at what point do we say "The overwhelming evidence indicates that ..."

At what point do we trust the opinions?

I found the following graphic on-line.  Click on the image to see it full size if it doesn't display properly in your browser.   I was surprised at how many learned groups had made these opinions known.  I am not going to state my own opinions here - I don't consider myself an expert in the field, but my training as a scientist does allow me to evaluate evidence provided to me in peer-reviewed literature.  It would be a very long stretch to claim that all of these individuals and groups were either supported by, or influenced by the companies producing GM foods.