(a) That's right. In this case, both A and B have made a mistake. It is important to notice that the mistake is not about the identity of the subject matter of the contract. The mistake relates to a quality of the thing - the age of the chest. Since mistakes about quality are easily made, the common law is reluctant to treat the agreement as voidable on these grounds. It will do so only if the error 'makes the thing contracted for essentially different from the thing that it was believed to be'. This is a hard test to satisfy.
In the current example, it was agreed to buy and sell 'an antique Dutch chest'. Antique items are clearly a different category of goods from modern items. Therefore the mistake DOES make the thing contracted for essentially different from the thing that it was believed to be. The contract would likely be set aside as void.