Light Yagami's interactions with his adversaries and allies in the anime "Death Note" are significant because they showcase his manipulation, intelligence, and moral ambiguity. His conversations with adversaries like L, Near, and Mello demonstrate his strategic thinking and complex mindset as he tries to outsmart them in the battle of wits. On the other hand, his interactions with allies like Ryuk and Misa Amane highlight his ability to maintain control and influence over others to achieve his goal of creating a new world order. These interactions ultimately shape Light's character and drive the narrative of the series forward, making them a crucial element in understanding his motivations and actions.