Why would you be doing a postcoital exam?
It seems like doctors don't use them very much anymore, but we had a postcoital exam to determine whether IUI was a good option or whether we should jump to IVF. A postcoital exam evaluates the cervical mucous and determines whether it is a good conductor for the sperm.
Thalia wrote in the comments (and I've added it here): There's a reason why doctors don't do these any more. The doctor I saw recently said, imagine a picture of a station after the train has just left. The postcoital test is like using that picture to estimate how many people got on the train. Enough said, in my opinion. If your doctor suggests one, ask why. If they insist, look for another doctor who has better kept up to speed with developments in fertility treatments [unless the test is being used to test the quality of the cervical mucous close to ovulation].
What to expect
Postcoital exams are conducted close to ovulation, when optimal cervical mucous is being produced. Simply put, the couple has sex (at home!) and comes to the clinic within a set period of time. A swab is inserted near the cervix to collect a sample of mucous. The mucous is analyzed and the couple is given a report on the quality of the cervical mucous. For the most part, the RE is looking to see how many sperm are still alive and moving in the mucous. And also the quality of the mucous (as well as quantity).
Problems that may arise and ways to troubleshoot
Except that you may not get to the RE's office in time? There really aren't many things that could go wrong with a postcoital exam. It's a simple, painless test.
The worst part of the postcoital is that it's embarrassing. In reality, all fertility tests and treatments are embarrassing, but this one is particularly blush-enducing since you just had sex prior to arriving at the RE's office. Some women drink green tea daily from CD 1 until ovulation in order to produce larger quantities of cervical mucous. I'm not sure if this is even a proven result of drinking green tea, but it can't hurt to down a cup or two a day in the days leading up to the test.