The saying goes Safety First, to which I disagree. Safety Always.
Batteries are incredibly dangerous if you are not careful. Ever feel how hot a AA or 9-volt battery gets when it shorts? Imagine what a car battery full of acid could be like. Read this http://rayvaughan.com/battery_safety.htm
about exploding batteries.
Never create a short between the two terminals of a battery, or drop a tool on the terminals, or let both touch the sides of the box at the same time.
The power that the inverter outputs is incredibly dangerous. This is the same voltage and current that comes out of the wall at your house. The 400 Watt inverter I used outputs ~3.5 Amps. Currents as small as 0.005 A to 0.006 A across the body can kill
Here are the facts about lethal electricity: http://hypertextbook.com/facts/2000/JackHsu.shtml
Now, don't let any of this information be off-putting. Taking all the proper precautions when working with electricity and batteries (like wearing Safety Glasses for starters) can help avoid damage to the components and serious injury to yourself.