Honda auto trannies are known to be pretty weak. But in some cars, they were pretty reliable, like in the Legends for example.

And the transmission being a little harsh in cold starts, that's normal. In fact, other cars I've driven had this similar effect: Toyotas, Fords, and etc. It's either by design or because the fluids haven't circulated properly throughout the engine/transmission. But you shouldn't feel much harshness once your car is warmed up though.