I've heard of course that probing mains can ruin your oscilloscope, so that is out of the picture. There are a few situations I do not quite understand however:
Is probing an i.e. 10:1 transformer safe if I were wanting to see mains signal? Even if it is not an isolation transformer?
If I cannot do the above, how does a wallwart make the situation different? Is ground being part of the linear regulator the device of which makes it safe to probe directly? Just anything that is not "earth" referenced?
Can I probe something that is on battery (silly question) with no earth referenced ground?
I've heard people mention something about the ground clip, and if it is not properly placed somewhere it could damage the alligator clip with large currents, however I have no clue what that is referring to, or how massive current could flow through the o-scope to the ground clip or something.
I am sure I could answer the before with some various manuals, however the ones before that I am just completely unsure of.