This more or less a funny question. When mixing the A and B component, i. e. the premix and isocyanate, the quality of mixing determines the homogeneity of the mix and the properties of the foam. You have to make clear to obtain a homogeneous mix. The load of gases in the mix is necessary to get the nuclei for bubble formation, their number is determined by the quality of your mixer. You have to consider that the A component is loaded with nitrogen before mixing with the B component which is also loaded with nitrogen. Nitrogen results from the purge gas of the single components.
Mixing is very critical in foaming for two reasons:
(1) as G Behrendt stated, it affects how homogeneous your mixture is (and when you're doing production runs, the residence time of the reactants in the mixer isn't that long, so the mixing needs to be pretty intense) -- so you want to mix well enough for this purpose;
(2) even for the same homogeneous mixture, more mixing = more work energy put in, so that the mixture starts out hotter and the reaction will happen faster (and that might not be a good thing if you want nicely controlled foaming with good properties; but if you want to use less catalyst, maybe this is a good thing that you can work with).
So for a given formulation, there is a desirable range of mixing intensity (and for a given setup and given formulation, the only way to affect this would be your mixer speed, as well as whether your mixing blades are clean - if not, you may have to burn it out). Outside the desirable range, you may either have poorer foam quality and/or foaming process issues.
What friends have mentioned above are all true. Only a very simple thing, polymerization of polyurethane is condensation type, so mixing is very important for reaction between isocyanate groups and hydroxyl groups. Foaming agents and the carboxylic acids for foaming process are next tips.
1- Indeed good mixing is important but since polyurethane components have usually a low viscosity it requires not such an intensive dispersive mixing as to generate heat or to get too much air in the mix. Usually distributive mixing is enough to get an homogeneous mixing. This can be obtained quite easily using the appropriate tools. Even static mixers can achieve a good level of mixing. They do not entrap air nor generate heat.
2- The hardness of the PU is determined by the crosslink density of the polyol-isocyanate mixture and the structure of the polymer (mainly aliphatic vs aromatic).
3- If you start getting air in your mixture you cannot control the amount of water you bring in, this water will react with the isocyanateand therefore you have a variability of the properties of your final product.
From your comment you do not say what are the quantities.
But say you are mixing a quart to a pint volume. You can use a 1.5" diameter impeller for a 3-4.5" diameter container at 1/3 of the bottom of the container. Increase progressively the speed until a slight vortex is formed. 500 rpm should suffice. It should not take more than a couple of second then to have a good mix.