Most law schools don't care a lot. It couldn't hurt to have a background in family dynamics. Finances also helps because there is a lot of that involved in dividing up families in divorces.
A lot of people going to law school major in the social sciences, so it won't really stand out.
Due diligence, also called document review, is the process of reviewing existing legal and business contracts of a business (including corporate documents, agreements and financial statements) for potential problems and issues prior to a proposed transaction, such as a merger or acquisition. The usual goal is to make sure that there is nothing in any of the contracts that would prohibit the sale of the company (or require a third party's consent) and to make sure that the contract will not terminate as a result of the sale. Usually, an associate will catalog the documents he or she has reviewed and write summaries of the key agreements. For example, when a merger is being considered and the acquirer hasn't had the time to read all of the contracts of the company it is considering purchasing, the lawyers will be expected to summarize the agreements. The purpose of due diligence is to give your client the clearest possible picture of the company you're examining, so the client can assess the risks and benefits of going through with the contemplated transaction.
In an initial public offering, due diligence involves reading agreements that are summarized in the deal prospectus—the document given to prospective investors summarizing important information about the company and the deal—to make sure the prospectus is correct. If you are representing an underwriter in a securities offering, you will review documents so that the underwriter can claim to have made a reasonable investigation of the issuer's statements in the offering document. Basically, it's done so that the underwriter will be able to claim the due diligence defense if there is a material misstatement in the offering document. ("I investigated and everything looked fine so don't come after me with a lawsuit because the investors lost their money.")