the transmission does not properly shift all the time into gear

Hello, When you have intermittent missed shifts, you are likely experiencing shift solenoid or accumulator issues, however, this may just be contaminated transmission fluid which is now an incorrect viscosity and composition. I do not recommend digging into the transmission to diagnose the issue, I recommend using a transmission specialist to diagnose the issue. Transmission specialists see hundreds, if not thousands of transmissions per year, and will likely know the issue after a test drive. Worst case scenario, they may need to remove the transmission pan to test and inspect.