The biggest danger is the artificial fertilizers, pesticides, and herbicides that are sprayed on many lawns. Lawn chemicals have been linked to malignant lymphoma, and bladder cancer in dogs, and hyperthyroidism in cats. Ingestion of these chemicals can also affect your pet's nervous system and cause symptoms such as dilated pupils, lethargy, and tremors. If you suspect that your pet has been poisoned by a lawn chemical or anything else, immediately contact the ASPCA Animal Poison Control Center at (888) 426-4435.
Another hazard of eating grass is the possibility of infection with intestinal parasites like roundworms.
If you just can't say no to that adorable face, try using a pet safe, OMRI approved product on your lawn, or you can grow some grass for them inside using wheatgrass seeds.