HEY! I need advice please. I'm working on a project where i have a stairwell and i'm trying to rig a Nimbus 2000 broom to float up and down it. I need a contimuously rotating servo because it will need to travel about 6 feet up and down, but a potentiometer because it needs to raise and lower to the same heights. I can currently set to raise x amount and lower x amount....but over time it will shift and eventually hit the end. Any advice on how to set a servo to lower a certain distance at a certain speed then return to starting position?
“ continuously rotating servo”
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These servos can be stopped by disconnecting the servo.
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Limit detection can be achieved using limit switches.
Welcome to the forum
You need some way of detecting the position of the object that you are moving or at least a way of detecting when it is at the extremes of its travel
I am not sure how the potentiometer is used in your project
I can't help but feel that you're trying to use a hammer to do a wrench's job, so to speak.
Every problem looks like a nail when you have a sufficiently heavy lump of iron. 
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That is exactly what you do not want to use, because all you can control is the speed of the motor, nothing else.
EDIT sorry also you can control the direction as @xfpd suggested.
What you do need is a stepping motor, with a reference detector position. Something like an opto beam sensor, or micro switch. Along with a proper driver for your stepping motor.
Otherwise your chances for getting a working reliable solution are zero.
- Direction
Can you do it now, manually? If so can you replace your hand power with a motor?
A sail winch servo can travel 3 rounds to exact positions.
That's not a reason to use a continuous rotation servo. Several other types of motor can also do that.
Why do you need a potentiometer for that? With a continuous rotation servo, you can control how many full rotations and what partial rotation is needed to achieve any specific height. How would a potentiometer be used to measure the height?
Why will that happen? I think you need to explain better how this motor will raise and lower the object. I am imagining the object attached to a wire or cord which is wound onto a drum or spool. By rotating the drum/spool, you raise or lower the object. How would that slip?
I can imagine a stepper motor would also work, but why would only that solution work while any other solution has zero chance of working?
I agree that some type of limit switch or sensor is needed to detect the "home position". Not because of slipping, but because any failure of the code or power failure would cause the Arduino to forget the currently achieved position and not be able to get back to the home position without "hitting the end".
But with that limit switch/sensor, several types of motors could equally be used, including a continuous rotation servo or a stepper motor.
A DC motor with gearbox could even be used, using run timing to achieve the desired position. However, over time, those timing errors would build up, unless occasional homing was used to correct those errors. An encoder or rotation sensor could reduce the need for homing, but the home position sensor will always be needed, I think.
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I am open to an other solution but skeptical as to if there is one.
All the requirements you raised are entirely valid, but have you thought about hysteresis in the mechanical system?
Most of these are the "relative" type of encoder, giving the well known quadrature output. However, there is the absolute type of encoder which could possibly serve as a position sensor. I used the AS5040 when I made a swinging pendulum harmonograph in the 2014 book "Raspberry Pi Projects" By Andrew Robinson & Mike Cook.
There are other chips in the same series that are probably more modern now.
This is an example of the sorts of results I got from it.
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Just found the video of this in action.
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I think we need to keep in mind that this project is moving a movie prop, so I doubt millimetre precision is required!
I'm going to guess... since OP has left the stairwell... that this imaginary, vibrating, broomstick will be in a school, ascending and descending a few floors, vertically, in the "well" (void) between opposite banisters and not diagonally, along the banisters.
A "simple" counter-weighted rope-and-pully with a reasonably sized DC motor and limit switches might work. No, a person can not ride on it (because that was going to be OP's next question).
- Then what’s the fun ?
- I think the mother in law could.