I agree with KM to place the sensor as near as possible to a white display area. However many screens seem to have an electromagnetic field that the oscilloscope picks up as noise. I assume this electromagnetic field is needed for the touchscreen to operate (though disabling the touchscreen in Windows didn't remove the noise).
One experiment I've tried is to have two probes - one not connected to anything (as a control) and one connected to the PWM detector that KM described in the other post. To make this experiment work, you have to move away from AC power (e.g., run everything on your laptop while in battery mode, away from the power lines in your house's walls).
In the screen shots below, the red lines are the PWM detector and the blue lines are a bare probe with nothing attached (control). Both probes are within millimeters of the screen.
Here is my phone. You can see that the noise is perfectly in sync between the two probes. From this, I believe you can infer that the light coming from the phone is a constant intensity, but the EM field generated by the phone is generating some noise.
Here is my wife's tablet (which gives me headaches). You can see that the noise does seem to be in sync between the two probes.
And finally here is my laptop. There is noise in both probes, but they're not in sync. But given that both signals are roughly equally noisy, I think you can infer that the light coming from the laptop has a constant intensity.
An obvious big source of noise is any sort of artificial light. Sunlight is fine, but other than that, make sure to turn off all lights.
And of course dbinv776 is correct that you don't want to touch any of the connections or the diode or resistor while taking a measurement. At first, I thought I could hold the wires in place and take a reading, but that didn't work.