Seeing parents date new partners is difficult for children, especially older children, and the new relationship may cause older children discomfort such that they decide residence with the other spouse would be more desirable.
When left up to the court, the judge will make a determination as to which parent should have primary physical and legal custody based on the best interests of the children, and if there is a real or perceived discomfort with the new parter experienced by the children, it is very likely to effect the amount of time each parent and particularly the dating parent is awarded.
If the new partner makes the children feel uncomfortable, whether it has to do with the partner personally or it's related to the children feeling that the partner may be at fault or contributing to the separation and divorce, this is likely to have an effect on custody decisions made by the judge.
As such, a spouse who decides to date during the separation is wise to keep the children and the new partner separate to avoid arousing these types of issues during the proceedings.
In addition to the possible financial or custody consequences of dating while separated, you may be subject to archaic criminal statutes that make adultery a misdemeanor.
During the proceedings, the fact that a dating spouse is already separated will be noted, but that does not necessarily mean the circumstances of the new relationship will not be considered.