The distinction between dynamic & static equilibrium
My answer starts with the premise that a static equilibrium exists (although that is debatable).


  How could we be sure that one certain reaction in equilibrium is dynamic?


If your reaction is at dynamic equilibrium, changing the temperature or the concentration of one of the reactant or product species (by adding some solute, for example) should disturb the equilibrium. You would see a net reaction, i.e. change in the concentrations of species in solution or in the gas phase. The reason you did not see any changes before is that the forward and reverse reaction were occurring simultaneously at the same rate.


  Since there would be no visible change in vessel, which property of the reaction would provide a proof besides color? Which laboratory technique could be used?


Color would not help either, unless you disturb the equilibrium first. Once you disturb it, any method sensitive to changes in concentration will give you evidence, as will calorimetric methods.


  [Devils advocate question]: What about static reaction equilibrium?


If your reaction is at static equilibrium, changing the temperature or the concentration of one of the reactant or product species, in contrast, would not result in any macroscopic change. For example, if you lower the temperature such that the forward and reverse rate are practically zero, and then add some reactant or product, nothing would happen. Not sure why you would call it a reaction equilibrium though when the reaction never occurs under these conditions. In other words, I know of no reactions where forward and reverse reactions suddenly stop with reactants and products still present under conditions where the reaction proceeded to reach equilibrium.