Without knowing what was said, it's hard to tell whether it was inappropriate or not. But since you said this occured in Serious, and the description of the conversation sounds rather casual, chances are it was.
As far as enforcing these rules is concerned, yes, things can be done. If no moderator happens to be in chat, feel free to PM one who is online on the user list - we're the green people - and ask them to come in. Sadly, we can't be everywhere all the time ;)
If that isn't an option, you could help us out a lot by
sending us a chat log of the conversation - even if you're not sure whether it's against the rules or not, it's better to be safe than sorry, and it's what we're here for, after all.
Hope you're well, take care.