An area where extra care should be taken while using your mobility scooter is during the entering, actually being in and the exiting of elevators.
As other people are using an elevator too, you need to take extra care and because you will be in an enclosed environment, even though only briefly, its important that you make sure that your mobility scooter is not able to suddenly jolt forwards or backwards during that time.
Entering an elevator at a slow enough speed to be safe, while at the same time moving into the space before the doors begin to close is ideal if you can manage it, fortunately elevator doors automatically detect objects in the way and cause no harm to the human body as they touch up against people so should cause no real harm to your mobility scooter if the doors do try to close before you are completely in the elevator.
If you make sure that your mobility scooter cannot move while you are in the elevator while the elevator is in use then you will keep the situation not only safe for yourself but for anyone else sharing the elevator with you at the time.
When it comes to exiting, depending on if there are people in front of you or not, it can sometimes be better to have others exit first, and to move slowly and carefully, keeping in mind that people on the floor that you have arrived at may not be expecting a mobility scooter to exit.
Give yourself a moment when you have fully exited the elevator to familiarize yourself with the floor and layout of where you are if you have not been there before, and then proceed once you know that it is safe to.