I STILL don't have my Mazda5, but I do know that many modern vehicles are mapped to maintain fairly high revs for a split second during a shift. This is to keep the catalytic converter warm, or promote rapid warm-up and clean burning. This means that your revs might not immediately drop when you lift throttle between shifts... so the effect is similar to driving an engine with a "heavy flywheel" effect. Of course the way I read what you're saying makes me think you mean the opposite -- that there is a stumble between shifts. I have never heard of that being normal.
I know that the 2.3L MZR engine had problems its first year with cold-weather starting, but I believe that has since been solved with a software remapping in later engines. Our 5's should be unaffected, I hope.