I used to monitor the reply address for a newsletter list with ~250,000 people on it. At this scale, a simple filter on "out of office" in the subject line really doesn't cut it.
To do it right, it's easily a full time job (and not a very fun one). "Noreply" addresses are bad for customers, but that doesn't mean they're always the wrong choice. As others have mentioned, it's better to bounce a reply than to accept it but not dedicate the resources to deal with it efficiently.
I used to work for a company that fed all replies to a custom CRM system which filtered out of office and bounces (unsubscribing on hard bounces automatically) and it worked great!
Those are enquiries from your (potential) customers. That's what you have support & sales people for!
It's strange that there are companies paying fortune to funnel people from AdWords to their sales enquiry form, but refuse to look at enquiries via e-mail.
To do it right, it's easily a full time job (and not a very fun one). "Noreply" addresses are bad for customers, but that doesn't mean they're always the wrong choice. As others have mentioned, it's better to bounce a reply than to accept it but not dedicate the resources to deal with it efficiently.