There are two extremes possible with examinations. They can be upheld very strictly, in an almost academic way, or they can be ignored altogether, as Annie Horniman discovered when she rejoined the Order after Westcott (the man who did much of the administrative work) had left. I don't think either approach is a good one, though I am more likely to lean towards the former than the latter.
You see, the problem with examinations is that they tend to be entirely intellectual, and, while this is an important aspect of our work, it is not the most important, nor the only part. Some element of practical work and testing on such is vital, as is a general inquiry as to how the grade energies have affected the initiate, if at all; afterall, if we end up the same as we did when we began then what is the point of doing it in the first place? So then we have multiple levels of examination, just as we have multiple levels to the system itself.
It is very important that our "magical ABCs" be learned. One of the best ways to ensure this is to test them. By committing the material to memory it can then be easily accessed during meditation; even if a Hebrew letter or planetary assignment momentarily slips our short-term memory it can be accessed via the sub-conscious mind. We are effectively building a vault within which we store the symbols of our tradition, a vault which we can access throughout the rest of the grades within the Order.
But I would encourage the student to do more than simply "learn by rote". Knowing that Aleph is the number 1, the Ox, spelled as Aleph Lamed Peh, etc. is too dry, too intellectual. Regurgitating material onto a page is not the work of a magician - anyone can do it. To know why the letter has these correspondences, and to discover new ones, is what differentiates the average student of occultism from a true magician. But in order to get to that stage the initial correspondences must be learned. In order for the Adept to develop a true and personal understanding of each of these symbols they must be learned in the first place in the Outer Order.
As for the practical element, this can be as simple as standing in front of people and performing a ritual. It is mind-boggling how many people get to progress through the grades without anyone every seeing them perform a ritual. While we can say "they are only fooling themselves", this is not really true - they are fooling the people who are letting them advance to the next grade. So why be fooled? Why make a mockery of the temple or Order by allowing someone advance beyond 0=0 if they cannot perform even a basic rendition of the LRP? Knowing the Knowledge Lecture is simply not good enough. The Golden Dawn is not an academic institute, even if it provides a very good academic knowledge of occultism along with its practical work.
There is then the issue of strictness in examinations. I admit that I would be reasonably strict with this, particularly in terms of the practical work. However, it is more important that one be able to carry out the practical work than get 100% in the intellectual examination. Mixing up two Hebrew letters is not as big an error as mixing up the names in the LRP or assigning the officers to the wrong stations. Thus I would be more likely to be lenient on someone who got a few percent (stressing few) under the requirement to pass their written exam, but would have no issue with failing someone who was unable to perform their basic ritual work.
As with all things in the Golden Dawn, balance is key. A good ritualist who does not know the Knowledge Lectures will be unable to explain their experiences, while a good academic will not be able to experience anything at all.