A valid contract requires one party to make an offer and the other party to accept. The offer must involve a "consideration" such as money, goods or services, not just doing a favor for free. In addition, the parties must both understand what they're agreeing to. A contract that lacks one of these elements is invalid. In addition, other issues can render a contract illegal or unenforceable.
If one party to the contract lacks capacity to make a binding agreement, the contract is voidable. For example, a senior with dementia, a mentally handicapped person or a small child lack capacity if they can't understand the meaning or effect of the contract they're signing. The National Paralegal Contract says that a party lacking capacity can still choose to honor the contract -- it isn't automatically void. In that case, the other party has no choice but to honor the contract as well.
The best lawyer in the world can't write a legally binding contract to carry out an illegal act. The Texas state government offers an example: two parties may have an oral agreement to deal illegal drugs, but if one of them reneges, the other can't go to court to enforce the deal. Likewise a loan agreement that charges more than the law allows isn't a valid contract, even if the parties thought they were within the law.
If one or both of the parties to the contract misunderstands the terms, this may invalidate the contract. An article in the Journal of Legal Studies says it has to be a significant mistake that hurts one of the parties, not something trivial or easily fixed. If, however, the party knew her understanding might be in error, accepted the risk and signed anyway, the contract may hold up. The Journal says determining which mistakes are significant enough to invalidate the contract is a major challenge in contract law.
Misrepresentation involves outright false statements, not just a misunderstanding. If, say, one party knowingly offers a fake Rembrandt as a real work, that's fraudulent misrepresentation. An owner who sincerely believes the painting is a Rembrandt is making an innocent misrepresentation. A material misrepresentation is one significant enough to influence the other party into accepting the contract. Material misrepresentation can be grounds for voiding the agreement.