I remember being very shocked when she died but I think that was just because it was so unexpected and she was so young and a similar age to me. I found the whole public grief thing very odd and quite uncomfortable. I was watching a documentary about it the other day and some of the people interviewed were reacting as if a member of their family had died, or at least someone they had known well. I was pretty neutral about her.
I think the fawning press coverage arose partly because the public were blaming the press for her death and so they didn't want to be seen to be in any way unsympathetic to her. As other pps have said, some of the papers were going to run stories on the Sunday which weren't favourable to her and these had to be pulled pretty smartish.
She was all over the papers and the "war of the Wales'" provided so many column inches for the tabloids. I think she did some good things with AIDS and landmines. As others have said, if you didn't live through the 80s and the stigma that was attached to those unfortunate enough to contract AIDS then you wouldn't really get the significance of her holding the hand of an AIDS victim. I was living in London at the time and had some very close friends who lost several people to the disease.
She also had her own problems and was by no means a saint and I very much doubt that if she had lived she would be viewed as such today.