It seems that this post has generated a lot of comments, some of which are extremely emotional. Hardly surprising since it's about food, one of the most intimate subjects for humans. Let me contribute my 2 cents worth.
As I understand from what I've read elsewhere, lab grown meat consists of two different types. On one side you have people who are trying to literally grow meat in a petri dish with cells extracted from animals. These are called cultured meats. The cells are put in a nutrient solution that mimics the actual food consumed by these animals in the wild. The cells are allowed to grow and multiply. The meat is harvested when it reaches the appropriate size. The other type of lab grown meat is based on the idea of mimicking the natural process. Instead of growing a cow which eats grass, then killing the cow to eat its meat, let's skip the middleman (middle cow?) and produce meat directly from the plant constituents (in this case, grass).
The concern here, as many people have pointed out, is how can consumers know that the meat produced in these ways does not contain other undesirable (or desirable, depending on your point of view) substances? What's to stop a cultured meat company from adding, say, contraceptives to the meat to control the population? What's to stop a government controlled company to add, say, mood altering chemicals to make their population more docile? A less sinister problem is government or companies adding, or not adding, fat, salt or other common (legal) substances to (mistakenly) control the health of a population.
Cultured meat can only succeed if it can get past the problem of trust. Unfortunately, in the present climate of mistrust, it will take a while to become mainstream.