Take pictures of the vehicle in the parking lot when you pick it up. The agent that presents the car to you is simply human and may have missed something, so it's better to be safe than sorry.
Should you be fined during your rental, you should pay the fine as soon as possible. If you do not, the agent you return the car to may charge you the amount, or your credit card may be charged.
Make sure you have the right insurance for where you are going. If you're going on rocky roads (or simply doing the whole ring road), take the Gravel Protection. If you're heading out to the south coast in spring time, take the Sand and Ash Protection. You can also ask the agent presenting the vehicle to you for additional insurance he recommends for your journey.
Also, read some of our articles on driving in Iceland before you arrive. There are a number of tips and tricks you should know before renting a car in Iceland.