Usually we arrive tired at our destination and the only thing we want is to quickly get into our rental car to be on our way. Unfortunately, trying to run might cause you problems and/or money later.
There are 2 fundamental things you need to do before signing your rental contract:
1) Read the rental contract and make sure you agree on all items, if you do not understand something, make sure you ask for more information.
The local rental company will usually try to sell you some extra insurance, some are interesting and are but that is up to you to decide. Personally I like windscreen and rims insurances, they tend to be cheap and if your are unlucky to get a crack in your window it will cost you a lot more. (NOTE: undercarriage, rims and windscreen are never insured, even with a fully insured car!! therefore some car rental companies sell this insurance)
2) On your rental contract any car damage has to be mentioned, so check your car, use the light of your mobile if you are in a dark garage, but do not sign until you are absolutely sure that any current car damage is mentioned in the contract, if you see a scratch or anything else that not mentioned, make sure it is added to the contract even if that means going back to the counter. The person giving you the car is not necessarily the person receiving you upon return. Never accept a verbal ok, get it on paper.
If you remember these 2 items when picking up your car, you might save yourselves a whole lot of trouble later. All together you will loose a few minutes to save hours of time and maybe hundreds of Euros later.
Have a good trip!