The 2004 Road King, also known as Dyna Superglide, is notorious for its faulty transmission system, incompatible engine, and the presence of fragile plastic parts in its main structure, which could pose safety risks. The 2006 Road King, known as Harley Electra Glide, presented challenges in maintenance due to its complex part assembly and had numerous complaints filed against it for various part issues. These models are best avoided to ensure a reliable and safe riding experience.