I have a 2013 Mini Cooper. Just had my oil changed. In the service menu it shows
 

I have a 2013 Mini Cooper. Just changed my oil . The service menu still says Needs Service. How do I clear the notice. Mechanic never-reset

Check your dipstick maybe they didn't change the oil...Just sayin

Owner’s manual

And if the did it my not be at proper level?

Has nothing to do with it. This isn't a "low oil" warning. It's a service reminder. My car has it too. The mechanic has to follow steps to shut off the reminder. It'll automatically go right back on again when the odometer reads whatever the next number is for the next service reminder.

I got my oil change at Walmart and they didn't turn off the reminder. I tried following the instructions a few times and eventually just stopped bothering. I know when I need to change my oil and I know when it's time for another yearly maintenance visit.

When the *warning* light goes on, I bring it to the dealer as soon as possible (within hours or - I bring the car home and don't drive it again until I'm driving it to the dealer).

It has everything to do with it. Just cause you had you’re oil changed don’t mean they done it right? Most owners don’t even know where the dip stick is, let alone how to properly check level. You want to follow up on any maintenance done, especially at dealership’s.

An oil change is not a service.
Post 2. shows how to reset reminder.

Really, so it not required?

Of Course. But it is just a small PART of a service.

Reset Service Reminder
 

Google it. I'm sure if you ask google someone will have a "how to" reset the service reminder notice.

Auto Zone will do it. Unless you want the Mini Dealer to do the Service.

That means it’s time to get a new car.

my father-in-law would have just put a strip of black electrical tape over it and been happy that he didn't have to look at it any more

Go back to where you had the service and have them reset it. Pretty simple.