It is safe to eat most street food in Istanbul. Depending on the season and/or time of day- options include roasted corn-on-the-cob sprinkled with spices, roasted chestnuts, kebabs, fresh fish sandwiches, pilav (chicken, rice and chickpeas, served with spicy peppers) and much, much more.
Care should really only be taken with the stuffed mussles, especially during the summer months.
Otherwise explore and enjoy the variety of quick and delicious street foods available all over Istanbul!