Eggs are safe, but should be considered with respect to a balanced diet. For a German Shepherd, the occasional egg (77 kcal) will not make a large change to their ration. A 90lb (40kg) shep should be taking in around 1700 kcal/d, more or less depending on activity level and whether or not it is neutered. An egg is about 5% of the daily ration. However, for a 10-lb poodle, an egg is about 25% of the daily ration of 300 kcal.
Remember that raw eggs contain avidin, which binds the important vitamin biotin (Vitamin B7). Eating raw eggs frequently can lead to biotin deficiency. Unpasteurized raw eggs are also a source of salmonella poisoning. I would prefer to feed cooked eggs to my dogs.
Eggs seem like a decent food for dogs, as they are high in protein and fat, and not too high in sugars. Wild canids often eat eggs that they find, and so it seems to be part of the natural diet. Many dog foods have powdered eggs in them. I would not feed exclusively eggs, or anything like that. Moderation and balance are important considerations for dogs. So, if you have a "treat" portion of your dog's daily ration, using egg for that treat is probably not a bad idea.