This could be an airleak after the airflow meter, any air dragged in here isn't 'seen' by the ECU and so not compensated for
causing rough running. The reason that this can effect the gear selection is the MAF meter is the main load sensor into the car and its input is used to calculate engine power and so make gear selections
As its a mechanical fault it tends not to turn on the fault light and you can sometimes hear a 'hissing' noise with the engine running.
Check the hose clips for tightness and inspect the trunking for any cracks or splits and also all the vacuum system, the small bore pipes and fittings for cracks and missing parts.
The best way to locate a leak is to have the engine running and warm and then spray lighter gas /propaneor brake cleaner around each joint in turn. If the engine rev's up you've found your leak.
Now you might think that spraying lighter gas around a hot engine isn’t wise, however the flash /ignition point of gas is about 400°C so you need a naked flame or spark to set it off and I’ve used this method for many years without incident.
Work your way through each possible joint one at a time and you should find it. I use a slightly flattened piece of brake pipe and some rubber hose from the can of lighter gas to provide a spraying 'wand' and allow a direct blast of gas into each area, especially those difficult to reach with large implements.
Air leaks are very temperature dependent as gaps can open up as things expand with temperature so depending on how the leak occurs ( on a hose joint with a clamp expansion will help seal and on a vacuum hose expansion ill make a leak worse) so leaks can be better or worse as the engine heats up.
1 vacuum leak path that you won't find with the above test is if the brake servo is leaking
so try clamping off servo hose to see if this has any effect
It’s also worth getting the fuel pressure checked as if this is low due to a blocked filter or faulty regulator or even a poorly pump will all result in insufficient fuel being delivered to the engine
Might also be worth cleaning out the throttle body as these get clogged up with carbon and some brake cleaner washed through helps free things off.
Might also be worth checking the wiring and connector to the airflow meter for any signs of corrosion or damage. you can do a quick fault find if you unplug the meter and run the engine without it.
if the engine condition is the same then chances are the meter or the connection to it is faulty
It’s also worth cleaning the MAF sensor wires, as they can get coated with dirt over time which then offsets the reading
Use some contact cleaner or brake cleaner to spray onto the wires to remove the dirt – on no account touch the wires with anything as they are very fragile
If the oil level hasn't been checked then that too should be done and the oil replaced if its black and sticky