Elizabeth, it is a good idea to separate your dog from the cats during feeding time to ensure that they are all receiving the appropriate food. Although it is not usually harmful if a small amount of the wrong food is eaten, nutritional imbalances affecting your pets' health could occur if this continues long term. For example, cats require taurine, an amino acid, to be included in their diet. They also need higher levels of fat and protein from meat. So, if your cats are eating mostly dog food, they could have nutritional deficiencies. On the other hand, if your dog is eating primarily cat food, he or she may become obese.
If you currently use the free-feeding method, where you leave food out for your pets all day, you may want to switch to the meal-feeding method, where you provide access to food twice a day for 30 minutes or so. This may make it easier to control which foods are being consumed.