Dating before the finalization of a divorce is probably a bad idea in theory.  In practice, however, many divorces take months, sometimes even years to resolve.  In addition, many couples have been disconnected from each other physically and emotionally by the time they file for divorce.  Thus, it makes sense that spouses in the midst of a divorce would start dating, or are perhaps already involved in a serious relationship.  Morals aside, this isn't normally something that would be relevant in a divorce case.  The purpose of the courts is to make decisions in the best interests of the children, and establish a fair division of the marital assets and liabilities.  

As a general rule, your personal life should not be a factor in these decisions, but there are a few areas where specific actions could affect the outcome of your divorce settlement.  The first, and most important area is custody and visitation, which is always decided according to your children's best interests.  While the court understand that one's love life typically does not affect one's parenting abilities, circumstances in your partner's life could be a problem.  If your partner has a criminal background, a drug or alcohol problem, or a mental illness, these would be issues that the courts would want to examine closely.  Choosing to be with such a person could give off the impression that you don't have your children's best interests at heart.  Even if you're not asking for primary custody, this could affect your ability to have your children overnight, or for any period of time without supervision.

The other issue, while less important, is still very relevant to the quality of your post-divorce life.  If it can be shown that you are spending significant sums of money on dates, or on a new lover, it could have a negative impact in areas such as alimony and the division of marital assets.  In fact, any lavish spending during a divorce -- even just on yourself -- could be seen as dissipation of marital assets.  Many divorcing spouses make the mistake of thinking that misuse or mismanagement of marital funds only applies when you're sharing a household, but fair and responsible use of shared assets is expected for as long you are married.

It's important to note that these issues are usually associated with serious and/or long-term relationships.  Signing up for a dating site and going on a few dates here and there should not hurt your chances of obtaining a fair and just divorce settlement.  The key element is discretion, and not engaging in attention-drawing behaviors such as lavishing your new partner with gifts, and posting about it on Facebook.  In the end, to date or not to date during the divorce is up to you, but the complexity your divorce, and the things you may stand to lose should make you think twice before inviting a new person into your life, as well as the lives of your children.