Denny - I've experienced #1 with English, lager, and Kolsch ale strains. The lager was the last straw. It wasn't side-by-side, but it was the same recipe, brewing and fermentation schedule. Cold crashed beer was noticeably inferior.
I think I've also experienced it in a saison, but I couldn't rule out other variables.
#2 is more a physical than a sensory observation. When all of the liquid in the airlock gets sucked into the carboy after cooling, there is obviously air introduced.
Overall - NOT cold crashing has NOT negatively affected my beer or process. OTOH, a slow rise in temp to finish fermentation followed by a slow steady ramp down to maturation temp has, IMO, made huge improvements. Other than a short gain in time, I don't see any benefits in a cold crash vs slowly cooling.