My kids often do this...
Fortunately, the elevator in the place where we live allows to "cancel" floor buttons when several have been pressed.
For this particular model of elevator, we can do it by very quickly pressing a button twice.
This was not explained anywhere in the building, I just noticed a friend once trying it in some other elevator.
It just happened to work, and I consider it a bit like a "secret cheat code" of the elevator.
So, during your long ride to the floor, try different button presses combinations (twice or more, long presses, several buttons at once, etc.).
You might discover the secret commands of your elevator!
lifehacks.stackexchange.com/users/1437/wip
someone had clicked the buttons for nearly every floor in the building.
I've been in many elevators (only newer ones, though - say, from the last 20 years)
in which when you've pressed the buttons for all the floors, they all get reset to unpressed/unselected state.
Probably worth a shot, since they're almost all pressed anyway.
lifehacks.stackexchange.com/users/5055/einpoklum
In some elevators there is a movable door sill for safety.
If someone gets stuck with his foot between the hallway and the elevator while the door is open, a ledge in the floor will act as a switch, resetting all buttons.
You can misuse this at your own risk, don't tell anyone you've heard it from me.
When the door is open, carefully put the tip of your foot in the gap of the floor between elevator and hallway and pull back the ledge.
These pictures are manipulated photos to create a simulation.
Many years ago I was living in an apartment building where I occasionally used this trick.
I don't know if elevators are still constructed this way.
Maybe it is only applied to elevator cabins that have no door of their own.
lifehacks.stackexchange.com/users/21787/Draakhond
I read somewhere that some lifts (that have been programmed so), long pressing the button takes you straight to that floor.
This is done by some manufacturers to cut short delays during emergency
For example, in our scenario, if you wish to go to floor 4, you could long press 4, and the lift would take you directly to the 4th floor without stopping at any other floor regardless of any button presses inside or outside the lift.
Though I've not tried this
and so I'm not sure if it'd work for your lift.
But it's worth a try.
lifehacks.stackexchange.com/users/21107/Sachin
It depends of elevator type, but some of them are allowed to be "reset", if elevator you use has a "STOP" button (or similar), then just press it few times.
It helps in elevator I use to reset all buttons to be not-pressed. :-)
lifehacks.stackexchange.com/users/21785/mariachi
Your proposed solution of getting off and waiting for another car makes sense to me.
Of course, you may just relax and enjoy the ride --- much better for the heart and mind than anger and unhealthy thoughts about the perpetrator.
lifehacks.stackexchange.com/users/6982/Alan
Just happen this with me a week ago,was going down As I was on 10th /F
found that no body was in lift and light was indicating up ^,
So I enter the lift and saw all button were pressed so when the lift door were opening on evey floor I try to press Close door button and it still save time because the lift are old.
Secondly In My campus elevator are new with new functions, If someone has press button so you can double press the button to remove/skip that floor.
sometime when a friendly teacher press the buttton students would double press to take teacher with them to other floor.
Laslty anyone worked as a repairman of elevator will know more about elevator tricks.
lifehacks.stackexchange.com/users/21804/Dream Developer
Take the stairs.
Really surprised no one has suggested this yet - get out of the elevator and hoof it!
You'll be more likely to save time if you're not going too far or if you're headed downstairs, but either way you won't have to deal with the frustration of stopping on every floor.
lifehacks.stackexchange.com/users/7679/Nuclear Wang
While staying in a New York hotel, I had the unfortunate experience of entering an elevator where someone had clicked the buttons for nearly every floor in the building.  At the time I simply got out at the next floor and waited for another elevator. However, I'm not sure what I would have done if there hadn't been a second elevator.  What can I do if someone presses every button in an elevator?
Somebody pressed every button in the elevator. What now?
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lifehacks.stackexchange.com/questions/17228
lifehacks.stackexchange.com/users/21777/Stevoisiak
If someone presses every button in an elevator, there are a number of different ways you can react to the situation. Some elevators are programmed so that long button pushes may cancel the request or take you straight to that floor. Other elevators may have a "stop" or "cancel" button. Failing this, you might want to just get out of the elevator and either wait for another one or just take the stairs. The options are to try different combinations of button pushing, use the door's safety ledge to reset all the buttons, trying holding down one of the buttons, press 'STOP' button a few times, relax and enjoy the ride or take the stairs.
If someone presses every button in an elevator, there are a number of different ways you can react to the situation. Some elevators are programmed so that long button pushes may cancel the request or take you straight to that floor. Other elevators may have a "stop" or "cancel" button. Failing this, you might want to just get out of the elevator and either wait for another one or just take the stairs. You could try different button presses combinations (twice or more, long presses, several buttons at once, etc.) or when the door is open, carefully put the tip of your foot in the gap of the floor between elevator and hallway and pull back the ledge.  Also some lifts have been programmed so that by long pressing the button takes you straight to that floor and It depends of elevator type, and some of them are allowed to be "reset", if elevator you use has a "STOP" button (or similar), then just press it few times.
Some elevators have a function that allows floor buttons to be cancelled when several have been pressed. This is sometimes labelled "STOP". Some say that a long press on the desired floor takes you directly to that floor. However, you could simply enjoy the ride, or even take the stairs. Depending on the type of elevator, there might be the option to cancel previous commands or go straight to your floor. Alternatively, you'll either have to just put up with the slow ride or get out and take the stairs.
Try different button pushing combinations such as quickly pressing twice on the same button. Use the door ledge to reset all the buttons. Try holding down one of the buttons. Press the 'stop' button a few times. Relax and enjoy the ride. Take the stairs.
Try different button presses combinations (twice or more, long presses, several buttons at once, etc.). When the door is open, carefully put the tip of your foot in the gap of the floor between elevator and hallway and pull back the ledge.   Some lifts have been programmed so that by long pressing the button takes you straight to that floor. It depends of elevator type, but some of them are allowed to be "reset", if elevator you use has a "STOP" button (or similar), then just press it few times. Your proposed solution of getting off and waiting for another car makes sense.  
Depending on the type of elevator, you may be able to cancel previous commands or go straight to the floor that you need to go to. You could just relax and put up with the slower ride to your floor. You could always take the stairs.