First thing to do is define bad culture. I would argue that a bad culture is one which prevents you from shipping products, shipping products that people want, or demoralizing the people who need to work as a team to ship those products.
Having tried to reform a dysfunctional culture and giving up after a while (because it was ultimately coming from the CEO and no one else had the formal or informal authority to change it), triggering events which caused me to move on were:
1. More time spent arguing over what the product should contain than would take to just build it and start over
2. Targeting a market despite already knowing that it was too small, based on inertia and political infighting
3. An office culture that values the appearance of productivity over actual productivity
Large companies can afford this more than small ones because they aren't bound by an immediate need to ship or die. But in a startup, anything that prevents you from either iterating on a product or raising funds is a warning sign, because you're on a runway and need to get airborne by the time you hit the end of it.