I figured, being an Oracle guy at a MySQL conference, this might be my only chance to answer something, so I went for the mic. Here is my answer.
The most common performance problem I see is people who think there's a most-common performance problem that they should be looking for, instead of measuring to find out what their actual performance problem actually is.It's a meta answer, but it's a meta problem. The biggest performance problems I see, and the ones I see most often, are not problems with machines or software. They're problems with people who don't have a reliable process of identifying the right thing to work on in the first place.
That's why the definition of Method R doesn't mention Oracle, or databases, or even computers. It's why Optimizing Oracle Performance spends the first 69 pages talking about red rocks and informed consent and Eli Goldratt instead of Oracle, or databases, or even computers.
The most common performance problem I see is that people guess instead of knowing. The worst cases are when people think they know because they're looking at data, but they really don't know, because they're looking at the wrong data. Unfortunately, every case of guessing that I ever see is this worst case, because nobody in our business goes very far without consulting some kind of data to justify his opinions. Tim Cook from Sun Microsystems pointed me yesterday to a blog post that gives a great example of that illusion of knowing when you really don't.