I have seen lots of discussion around here about safe probing using either a differential probe or an isolation transformer on the device under test. I have also seen mention elsewhere of the old school method of using 2 probes with the add function and inverting one of the channels. It also seems that in a pinch a voltage meter could be used to check for a difference between scope ground and the ground point of interest on the device under test before probing, and simply not probing where there is a significant difference.
What are the possible issues with these various methods of probing? For example, I saw one mention that using the scope's add function for differential probing will be noisier than using a differential probe.