While I sympathize with you that this was disgusting at best, I wouldn't characterize this as the worst experience ever. You got to your destination and it doesn't sound like there were any issues with your reservation, maintenance, etc.

I don't even know if I would classify this as an overall service failure at UA either. I don't know what you expected; you made the FA aware, even after the door was closed your wife made it a point to request the passenger was removed and they were. Maintenance came and attempted to clean, but apparently that wasn't enough either.

You say the gate agent made facial gestures, but standing behind a counter its not like the agent was physically inspecting the passengers clothing. Then again not sure what the FA could have done either. It's a crappy situation (no pun intended), that airline staff face when they have to confront a passenger with hygiene issues because of the sensitivity that the passenger could claim a number of issues either discrimination, being singled out, etc

I'm not saying its right for someone to sit in their own filth, but consider that there are a number of issues that could be at play here. What was their mental capacity, did they have a change of clothing, were they unaware of the problem. I have a hard time believing that this was matter of public safety....gross yes. But consider that if the problem started inflight its not like they are just going to divert to clean up poop or throw the passenger off.