No on the "stars" because in my experience standardized early education curricula usually look like a lot of papers and seat work and they've got 13 years of school for that. I would rather a place where the director understands that learning comes through play, where they kids are up and moving around for most of the day, where there is ample opportunity to play with sand/rice, water, clay, finger paints, scissors, pipe cleaners, gluing wiggly eyes on things, etc. Lots of music, dancing, and reading books while sprawled out on the floor. Plenty of time to go outside and play on a play structure pretending to be pirates and princess, doctors and cooks, etc. So a "Star" system would be of no value to me unless the department who designed actually managed to break free of seat work and embraced learning through play.
While I don't care whether or not all of the teachers have EE degrees, I do care that the director and lead teachers do. A home daycare is totally different but for a center, I want a highly educated director who hires and trains excellent teachers, and educated teachers who can help train teachers who don't have a degree and ensure best practices for those who come in with years of experience but no formal education.