So on my 02 accord, when I go out in the morning, it doesn't shift into 2nd gear as smoothly as later.
This is only on cold mornings below 45 degrees. Once it makes that first shift of the day, it's fine the rest of the day. My wife thinks the transmission is in it way out, but I think it's fairly normal for a 14 year old car. It only does it when it's cold and cars do weird things like this in cold weather. Opinions so I can prove her wrong or admit there might be a problem?

 

When it is cold out, or the car is cold, the shift logic is different from normal operating temps. Usually the shift is delayed and will be harsher due to the later shift/higher rpm. This is to reduce load/wear on the engine when it is cold. If the car was allowed to fully warm up before driving, albeit the shift would be normal.