Sounds like you don't want to go with the traditional methods of testing (of which volumes and volumes have been published). Here's my .02 non-traditional approach:

for users finding something wrong: have good logging - don't depend on the users for 100%. Write decent well formatted and consistent error messages so log parsing will be easier.

for missing features: have a good user feedback mechanism - have a "report problem/suggest feature" link on each page. Also make sure the copy "leads" the users to use the link (don't bury it - at least not in the begginning).

How to make it faster. Combine the logging with good timing stats. You should have an inkling of where your bottlenecks will be (database calls, transforming xml, etc). Start logging those hotspots to generate some stats. Maybe they are bottlenecks, maybe not - you'll need some historical data to let you know what's normal and what's not.

I think if you have consistent well thought out logging (that includes having the mail go to some alias with a canned subject) you should have the foundation necessary to programmaticaly monitor the health of your app.

-derby