At some point, those errors can become costly. Misbehaving applications can cost serious amounts of $$$ when your business relies on them, but testing every page in every way possible isn't necessarily possible, either. Error logs can help, but dont always tell what the user did.
As we're moving this time, I installed a Coradiant TrueSight. This 1U server monitors and logs all inbound and outbound communications, giving real time reporting and monitoring of all pages. It may be pricey, but not having it could be even more costly. I'm glad we had the available funds and management that could see the value.