The are two main weaknesses with radiosity; computer load and specular surfaces, but there are ways to go about this
Computer load
An interesting approach to go about this problem is to implement methods such as the Monte Carlo method, which alters the exactness of the solutions to the energy equations calculated.
Specular surfaces
Even if the radiosity method results in almost perfect diffuse surfaces, the specular aspects of reflection and refraction is obliviated. This can be solved by also using the ray tracing method wich results in perfect specular surfaces but leaves the diffuse virtually untouched. Thus, combining these methods enhances the result.
A second way is to use enhanced versions of the ray tracing method, such as Two pass tracing