Any large scale synthetic meat production would probably be prone to deviations, cell division is a failure prone process and there's no immune system to destroy anomalous cells in the culture, but food quality regulators would probably catch anything important before a given batch was sold to the consumer.
Fundamentally there's nothing about synthetic meat that should be more problematic than meat grown the old fashioned way, all the potential health risks can arise in livestock, plus a few extra ones unique to live animals and poor farming practice.
The problem I see with synthetic meat is that it won't ever actually be quite like the real thing, which will affect what kinds of dishes can be made from it. A synthetic meat slice has similar texture to a thin piece of lean meat, and tastes very similar, but the absence of things like adipose tissue, little bits of connective tissues, bone marrow and so on means it's not a direct translation of a chunk of meat from an animal. You couldn't make a duck confit out of cultured duck tissue for example, or oxtail soup from cultured beef.
Obviously this isn't exactly a super important problem, the availability of specific flavour profiles and dishes is hardly a world ending issue but I do think synthetic meat culture will only work as an additive to conventional, though hopefully more humane, meat farming because it can never fully satisfy the demand for meat.