So. The answer is that yes, there must have been. We have limited evidence for the public toilets, and none that I can quickly link you to right now. Some (anonymous) websites claim that there was a complex drainage and therefore sewage system from the site. This is not necessarily accurate. Drainage does not have to equal sewage. There were public toilets in Rome, and it would be unusual for there not to have been in the Colosseum, whether it held 50,000 or 73,000 (alternative figure, less likely).

A recent(ish) monograph from Ann Olga Koloski-Ostrow (2015) has examined the issue of public sanitation in Roman Italy. As a counter to that website's claim regarding the drainage meaning sewage, she argues that Rome's drainage system was better suited to being a storm drain, to prevent the city flooding. More common were cesspit type toilets. Unfortunately, given the nature of the Colosseum, I am not sure we will ever really have a definitive answer, but one thing I think we can be certain of is that you should never use a public toilet in the Colosseum, ancient or modern. They're not pleasant places.