This question already has an answer here:
We all know what happens when we ground a regular oscilloscope probe at the wrong place: a short. There are two main points to consider:
1) All channels share the same ground plane, so we can't take 2 or more simultaneous measurements referenced to different "grounds".
2) The scope's ground plane is directly connected to the center pin on oscilloscope's AC power cord, which is probably connected to the ground of the equipment we are probing, preventing us from using any other reference than the "official" ground itself, otherwise we will have shorts and possibly fireworks, in more severe cases.
There's nothing to be done about point 1, but about point 2, why not simply disconnect the center ground pin on scope's AC cord and leave it floating? I personally do that with my older scope. When using channel 1 only, I can freely move my ground hook everywhere in my circuit, and I never had any problems, apart from some 60Hz noise, but this is expected, I guess, since the whole scope is floating and subject of all kinds of noise.
So, apart from the increased noise, is that harmful to leave the scope ground floating? What else am I loosing doing things that way? In which situations my practice will bring me serious trouble? Does that damage the scope in the long term?