I wrote a couple of paragraphs which I ultimately cut, partly for space (I went rather longer than projected on this one) and partly because I didn't think they quite fit. But for anyone interested, here they are:
Persistence in the face of repeated failure in the exams posed certain problems for administrators. The nominal age of retirement from the civil service was 70, but there was no formal age cut-off for the exams; it would be disgraceful for seniority-loving Confucians to turn away the aged. Therefore, very old exam-passers were accorded special treatment. Men over 70 were graded more leniently than their younger brethren, and if they passed, they were granted honorary titles, though not actually put in office.
At various point in the cycle of exams, candidates had to answer questions written by the emperor himself (or, at least, ghost-written and sent out under the emperors name). This posed additional problems for test takers. The candidate had to be careful to avoid using characters used in the emperor’s name and in the names of any member of his dynasty. The emperor’s name was regarded as sufficiently sacred that using bits of it was regarded as criminally disrespectful. Fortunately for the candidates, Chinese has enough characters that one could substitute characters producing the same sounds, but it was one more detail to watch out for.
This article is mostly world-building material, but it implies a variety of adventures. Going anywhere in the ancient world is difficult and risky. An adventure or series of adventures could be built around a group of friends trying to get a candidate for office to the testing location on time. Under various conditions (usually when heading to the more advanced tests), candidates had permission to travel by official vehicles rather than on their own yuanbao, but even then, if bad weather or uncooperative officials intervene, individuals must find a way to push through. Ghosts and other supernatural critters who appear at exam time may need to be appeased or otherwise dealt with. Cheating attempts are the perfect venue for Ocean's 11-style capers (and, of course, the caper-y and the supernatural combine; what if, as the surviving Imjin War veterans assemble at the funeral, the dead one pops up from his coffin full of forged exam papers as a hopping vampire?). And all of this can just be setting the groundwork for a higher-level intrigue campaign in the civil service. The stakes for the exams are largely personal; once the candidate attains office, they become political as well.
(I realized that I'm posting on GURPS-Day, but since I'm writing now on a topic which has only tangential GURPS content, and it's essentially coincidental that I'm posting on the right day, I didn't throw my hat into the ring to be listed for GURPS-Day posts.)