Is Trader Joe's responsible for their cart damaging my car?
It doesn't matter if they have a sign or not. They can not contract away or otherwise exempt themselves from negligence. Many businesses post signs that say they are not responsible for certain things, and by the answers herein, you can see that the businesses are successful in making the people believe that they are not responsible. By posting the signs, they have been successful in persuading 90% of the people not to file a claim. Of course they are liable for maintaining dangers on their property that they know will cause damage. A business that owns a parking lot has business insurance that, in part, insures for "premises liability." As grocery store businesses are held liable for parking lot signs falling on automobiles, they are liable to customers for property damage that they invite onto their property. One would hope that if you asked the business to file a claim under their policy that they would. Otherwise, a business that asks their customers to come onto their property and provides them with a parking lot will be held liable for not making it reasonably safe for the customer or the customer's property.
If someone signs a contract (eg lease) but enters a coma or is declared mentally incompetent and committed..?
No he is not of legal mind and sole to care for the obligation, They may still attempt to get it filled, and may even try to get family to. They are not legally committed to pay it.
Does a "not responsible for Damage" sign clear a carwash if damage is done, or is this a tactic on their part?
A unilateral disclaimer is usually not a bar to attempting to recover valid damages. Some jurisdictions may take the view that it is a contract offer, and you accept the terms of the offer by using the service. A sign that disclaims ANY liability for ANY damage might be interpreted as being too broad to be enforceable. The carwash that I use disclaims liability for non-factory installed equipment and goes on to list several examples "such as": antennas, spoilers, mirrors, ground effects kits, etc. as well as power antennas that are not fully lowered before entry. That disclaimer is much more reasonable, especially as it applies to items that may be outside of the typical design criteria for a car wash. If you can substantiate neglect on the part of the carwash operator then you might have a case. Proving neglect could be difficult. If you have comprehensive insurance coverage, it might be worth filing the claim with your insurance company and letting them go after the car wash. You could try filing in small claims court if the damage is less than or only slightly over the small claims limit for your state. Otherwise, you'll need an attorney to proceed. In fact, it may only take a quick letter from an attorney to prompt the car wash owner/operator to pay up and avoid an expensive legal battle.
Can I make a woman sign a contract before sex?
No court would enforce it. If you father a child, they're not going to make the child suffer. You may have a lawsuit against the woman for damages, but the court still isn't going to screw over the child at the end of the day. If you don't want to have kids, don't have sex with people who are going to play games like this. And don't have sex with anyone unless you're willing to deal with the consequences that can arise, be they kids or otherwise. The species continues because kids tend to get born no matter what. You might be better off if you realize that all those sexual urges you have are kids just trying to find a way to be born. And all those women who want to sleep with you? Their bodies are trying everything possible to get pregnant. Your mind might say you just want to have fun without pregnancy... but that's just a trick of the kids trying to be born. The number one reason sex exists is to make babies. Keep your pants zipped up if you can't handle it. No "contract" is going to protect you.