In the bath scene with Capucine and Robert Wagner, an industrial-strength foaming agent is used, which burned both of the stars' skin. Wagner, who was completely immersed at one point, became blind for four weeks.
At the start of his first visit with the Princess, Sir Charles Lytton is using his cane on the left. Within minutes, he's switched it to his right. This could just indicate that he's playing up the injury to spend time with her.
According to the film, the diamond gets its name from a flaw in the colorization, because it is slightly pink, and when held up to the light, it is possible to see a panther-like figure inside, hence why it's called "the Pink Panther".