I had a pretty awful experience with them at GCSE level - out of my 11 subjects, 4 ended up having their grades changed, including Geography going from an E to a B. I decided to take the International Baccalaureate instead of A Levels (not just because of this issue, but it is a bonus) and from what I can see the exams their are much more consistent year-on-year, grade inflation is next to non-existent (one point out of 45 over nearly 40 years), and there seems to be a much better correlation between how well people perform in class, their mock results, the amount of revision they do and what grade they finish with. This is despite having the additional issues of a linear exam system (much less opportunity to resit, making it crucial that the exams are right first time), a greater scope for language barriers and different time zones (meaning each year they must make more than one paper per subject so answers aren't put online before people elsewhere in the world start the exam).
For GCSE/A Level, I would suggest many changes. I would scrap the exam board system and replace it with state-sector agencies setting both the syllabus and exams for each subject. These agencies would have representatives from areas candidates taking the course in question are likely to go into, such as universities and employers, depending on exactly what the course was, so that the exam was set by people with a genuine knowledge of the subject at hand who also know what skills they want successful candidates to possess, and also removing the ridiculous competition to make money through putting out easier exams, or charging silly amounts for re-marks.
I would try to reduce the need for remarks by appointing only university-level professors as examiners - we can quite easily get them to do this as the vast majority are still public sector. Each examiner should also have around 10% of their batch also marked by a second examiner, and if there is a significant difference in a large number of papers then their whole batch should be referred to a senior examiner to mark. I would then provide photocopies and remarks of papers at-cost, with a full refund if there is a difference of more than around 2% in the new mark compared to the old one.
In terms of coursework, I would make schools/colleges/whatevers send off everyone's, from which a random proportion are moderated. This means that they don't know who's will be checked, so they have to make sure all pieces have been marked accurately and honestly rather than just those pieces they are told to send off. A consistent failure to mark it appropriately should be noted in Ofsted inspections (I haven;'t talked about those lot yet but rest assured I am plenty critical of them too :P )