Your first best bet would be to enable slow query logging on your production mysql server(s). This feature is described in the manual.
You can also get Apache to time (in miliseconds I think) how long each request took - this is particularly interesting for small PHP pages which take a long time. This log will of course be quite large, you might need to write your own tools to analyse it.
Other, cleverer options will involve doing some more performance testing in a non-production environment. You will need a data set of the same size as your production data in such an environment - if your organisation permits it and it's possible, I recommend that you take a dump of the production data into your test environment.
Your test environment should obviously consist of production-grade hardware (and NOT be virtualised, e.g. with vmware).
You can then throw requests at it and measure in a production-like environment, how long they take. You can also add instrumentation either in your code, or using something like APD (whcih is a zend extension), neither of which you would be able to do safely in a production environment.
Moreover, a performance test environment allows you to check whether a proposed improvement will actually help, before putting it live. This is pretty much vital.
If you are doing frequent builds and it's an important site, I really recommend that you build some kind of performance regression testing facility - this will not be easy, but it will enable detection of (some) newly introduced performance problems before they reach production.
Finally, you should probably have a procedure for rolling back each software change to your production environment (in case it turns out to be disasterous despite the above testing), and/or a facility to turn off specific features in production.
Mark