2003 Gran Prix, 200,000. Shifting from 1st to 2nd does or does not happen depending on conditions. No problem with any other shifting. I have been having problems for a few months now:
Air temp 60+ & engine cold -- bad, will not shift into second for maybe quarter of a mile. Once it makes it to 2nd most subsequent shifts from first to second are ok. The more the car warms up the better behaved it is.
Air temp <50, problem exists but significantly less of a problem.
Have found that gradual starts from a stop help it catch.
I took it into a transmission shop and they said the codes indicated my car was a mess, the transmission needed to be replaced and probably was not worth it. Sorry, do not have the codes.
It occurred to me, when the weather got cold and the transmission started to behave "better", that maybe something else was going on, like a bad temperature sensor and thought I would ask the question before chucking $3000 at the problem.