What is the loss of productivity of not using the international system of measurments (SI) The USA and some other countries are not using the SI-system. Are there any estimates of how much productivity is lost because of having to convert numbers? (non-SI countries, SI-countries)

I imagine that the loss not only affects the non-SI countries, because the SI-countries wanting to export to non-SI countries would also use time for conversions in order to comply with local laws and customer demands.

The costs are probably difficult to measure because they are small amounts that are across every industry. For example car companies having to switch the km/h to mph speedometer; schools that have to spend much more time on explaining the non-SI system; or the the many goods that need double labelling.
This is a good example of "transactional costs" -and of the small "menu costs" as Mankiw has once called them. His paper Mankiw (1985) "Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly" The Quarterly Journal of Economics, 100(2):529-537 contains a model where in his own words, shows that "sticky prices can be both privately efficient
and socially inefficient." 

The basic mechanism of the model is as follows: a monopolistic firm has to set the selling price one period in advance, based on expectations about future demand. If demand is realized lower than expected, the firm can reduce its price but at a "menu cost" (alluding to the costs that restaurants have to bear in order to re-print their catalogs with new prices).  

Mankiw shows that even though this cost may be small, still it may prevent the firm from adjusting the price. So prices become sticky, which is socially inefficient.  

Of course this is an underlying theory that justifies the existence of inefficiency due to such "transactional costs". Actually measuring and estimating them would require a detailed audit approach as regards the time spent and other costs involved to change measurement units.