I saw 2 Yorkies today on the back parcel shelf of a car heading out of my local supermarket. Is this safe?

Not at all safe. Even if we assume those dogs only weighed 10 pounds and she were going only 30mph, that is 300 pounds of force that those dogs would fly. If she were going faster, then that number is multiplied to a greater number. Imagine that much force hitting the driver or passenger in the back of the head. For small dogs, you can use a dog seat belt or even a pet car seat. Kurgo makes both in safety tested versions. Bergan and Pet Buckle make safety tested dog seat belts. Bergan is also available in the UK. (My dogs Maya & Pierson use the Bergan dog seat belts.)

Not safe if anything it can be a distraction to other drivers. The owner should have the dogs in a proper pet seatbelt or carrier to avoid injury. If the driver were to get in a crash the 2 dogs would be injured or maybe even dead.

I've seen this in my area too, or even dogs sitting on the front dash while the owner drives. Its dangerous for the dog and dangerous for the drive, and I can't understand why people think its okay. My boy either lays down in the back seat or sits up front with me with a doggy seat belt on. If you wouldn't let your kids do it, you should let your dog do it.

no that is not a good idea @ all the poor little things they could fall or get really hurt. not a wise choose so i would hav told them to put the dogs in the front seat or inlike a cage or something. poor puppies i hav two chihuahuas.

NO WAY WOULD I PUT ANY LIVING CREATURE IN SUCH A LIFE THREATENING POSITION!!!!!!!!!!!!!!!!!!!!!!! I would use a dog seat. get it @ a pet store.