In a thorough diagnostic work up, these strengths and weaknesses are examined further by using specific tests that "go deep" into these areas. For example, a psychologist would probably give a child additional tests of visual memory and visual motor performance, such as a shape-drawing task, to get a better understanding of a weakness that showed up on the Block Design sub-test on the WISC-R. Similarly, other tests would be given to look at the child's auditory (listening) skills, and so on. As a neuropsychologist, I interpret the test results with a focus on what they tell me about which areas of the brain are involved. In this way, it is possible to identify more specifically the type of LD that a student has, and what methods have been shown to be particularly helpful for that constellation of skills.
The Woodcock-Johnson Tests of Achievement can tell us how well a student is performing in traditional academic areas when compared to hundreds of other kids. So, it will do exactly what you said confirm a problem. The skilled clinician analyzes how a student approaches the tasks on such a test, a technique that provides information that is much more important than a child's grade equivalent in some subject area. This kind of micro-analysis is often done by special educators (trained in the use of this test) or psychologists who specialize in the assessment of LD, but may not be done by a busy school psychologist who has to test 20 kids a week.
On the other hand, the Woodcock-Johnson Tests of Cognitive Abilities correlate well with IQ tests and can be used in place of the WISC test. In fact, these two different Woodcock-Johnson tests were developed to enable a tester to efficiently look for gaps between intelligence and achievement. These are well-respected tests, but to use them to their fullest, the diagnostician has to do more than feed the scores into a computer for a mechanical analysis. In much the same vein, a medical doctor couldn't fully make sense of a lab test without physically examining the patient. Most professionals would agree that as good as they are, the Woodcock-Johnson tests are not sufficient to make a diagnosis of a learning disability. The results may hint strongly that such a difficulty exists, but a more refined battery of tests is usually indicated. A complete examination also involves observing the student as he or she completes real, everyday learning tasks. A skilled special educator can do a very effective job at assessment of LD, by using an approach called curriculum-based assessment.
In short, the diagnosis of LD is no easy matter, since there is no single test or battery of tests that definitively confirms this condition. Someday we may have brain-imaging equipment that will help, but right now those techniques are only in the development stage. In the meantime, the experience and skill of a seasoned clinician are the best tools we have.
My advice on preparation for college entrance exams: If the LD is confirmed by a professional, your son may be eligible for special accommodations, such as untimed testing or a scribe (to write down what he says). These accommodations depend on the nature of the LD and its impact on tests like these. Your son may also find it helpful to learn better test-taking skills, either from a series of workshops in his high school or at a commercial test-preparation center.