Connecting and disconnecting the power supply
Its not quite the rule that ground should be connected first, instead the rule is generally power before data, If you look at a USB plug / socket you will notice the 2 outer power/ground connections are longer than the middle data connections, Same for Micro-SD card,

In these cases by having the device be powered before its connected to data lines means everything is at a known state, there will not be any pins mid way from raising from a low to a high signal. 

What it sounds like your describing is a mains ground loop, things like PC power supplies have there ground tied to mains ground, so by having your UART - USB Cable connected, they share a ground, if your ground referenced power supply looses its ground connection to your circuit, It ends up completing its circuit through the wiring in your walls

In reality it is rare for this to damage a circuit, however it can make it act weird as this tends to couple in a fair bit of noise.