Warnings

Read the warning labels on the case and internal components Microsoft puts those there to indemnify from responsibility because it is in fact dangerous in there. The power supply is exposed, when it is not plugged in it can still hold a significant amount of power, it can shock you, if it is plugged in and you touch it, it WILL shock you. Taking proper precautions it can be perfectly safe. A few things to consider.

Damage to you-
High voltage electrical shock hazard, touching almost any part of the power supply while it is connected will result in a shock. Even a brief shock at just the right moment/voltage etc can result in messed up heart rhythm and death. Consider wrapping the power cord into a bundle, when the case is open the cord stays under the lid in a bundle. When the lid is on you can un-bundle the cord and plug it in. This may sound like an exaggeration but you need to be very responsible with your actions.

Damage to your Xbox-
Some good info on Electro Static Discharge ESD.  Put on your pink fuzzy slippers and slide across carpeting dragging your feet while wearing wool... Then start working on your Xbox!?!? no no no... 

Science lesson for the day, Low humidity increases static charge build up (more accurately it decreases the ability for the air to dissipate charge), movement of one object across another creates a difference in static charge. You know what clothes you have that create static electricity, don't wear those when working on electronics.  Its not the static charge that causes damage to electronics, it is the difference in charge, and specifically the rapid change in charge that damages equipment.  

Each ring represents an object... any object, lets think of one of them as you and one of them as your xbox, regardless of whether you are positive or negatively charged or both objects are either positive or both negative, the charge wants to equalize itself when the two objects meet.  AKA static spark.  You don't need to create a spark to do damage to your precious electronics.  Imagine an aquarium with a divider in the middle, one side is filled half way full and the other is filled completely full, if the divider were suddenly removed the water would slosh in both directions until it equalized and again became still.  The trick is to see your xbox is not the aquarium!  

The most common method is to ground oneself this guarantees that you are at a lower potential than the equipment you are working on, any static charge leaves the equipment and enters you.  This can still cause problems so ideally both the equipment you are working on and yourself are grounded.  For safety reasons use an approved static wrist strap, these are designed to "break" if too many amps go through them (you don't want to become a lightning rod for your AC house current)

In the Llamma Lab we have ESD certified grounded tables that are designed to dissipate static, we use wrist straps and have a simple alligator clip that is attached to the metal part of the case.  The person working on the system, the table and the equipment itself all are at the same potential.  When we are working on a package or system we take all the necessary precautions to see it is not damaged simply by handling it.  But that is only half of the battle, you must take the same precautions when installing our equipment to enjoy trouble free play time from your console.