The key takeaways from TechCityInsider's podcast on growing startups globally are that relationships with local companies and culture should be prioritized over scalable practices initially, and it's essential to develop a deep understanding of the specific needs of your customers in each locale. To succeed, you must adapt to local expectations, stay connected with your customers' preferences for products and messaging, and leverage the tight-knit tech community in London to build connections and opportunities. The challenges of expanding globally include finding the right talent and building brand awareness in a new market, but successful companies like Flood Hack demonstrate the power of community-driven initiatives and collaboration.