Oscilloscope ground oscillating
An oscilloscope is a differential device. When a signal is applied between the ground and input of the scope the display is the difference of the two. Lets call the scope ground, REF to eliminate confusion with earth ground. The differential input is awesome because REF can be connected to many places other than 0V to inspect signals that wouldn't be seen otherwise. 

The greatest problem is that in all scopes (except specialty ones) the REF is connected to earth ground (GND) through the power cord. This grounding necessitates that either the scope or the device under test (DUT) be floating. If neither the scope nor the DUT are floating, connecting REF to something hot will create a short and blow the ass out of your scope. 

There are two test setups that are needed for proper testing. At least one needs to be met so your scope works well and does not explode. If both are met there is no problem. 


The DUT is floating. This could mean that the DUT is battery powered. If the DUT plugs into mains power than the use of an isolation transformer is needed. 
The scope is floating. This could mean that the scope is battery powered or plugged into an isolation transformer. 


When connecting a floating device to a non floating device the floating device will reference itself to the non floating device. If the non floating device then has variation in its GND the floating device will simply move up and down, sort of riding the wave. You will never see the change in GND. 

Even if the scope probe is shorted to REF directly all this would show is that there is no input offset. This is because, again, if there is a variation in GND the differential input will simply ride up and down with the variation always showing nothing. 

From what you describe, i'm gathering you unhooked the probe and left the scope alone. This will show you garbage. With the input not connected to anything, it is floating. With a floating input the scope picks up crap from the environment. Attach a probe to the scope, short REF to the signal on the probe. If the signal stays at 0V then your scope is fine.