One change in particular from 2006-era WoW to WoW Classic has been pretty highly reported-on: skeletons no longer permanently mark the spot where a player dies.
The senior test lead explains,
While we understand that this was a flavorful part of Original WoW and the earlier expansions, individual players leaving multiple player corpses and skeletons throughout the game world can lead to behavior such as spelling out advertisements, hate speech, and other negative messages. As such, this will not be a part of WoW Classic.
(As IllusiveBrian points out, you still do leave a skeleton, but it only marks the spot of your most recent death. They no longer act as permanent parts of the landscape.)
You can actually see all questions any of the developers answered during this AmA here, and it provides some interesting further information on changes. Basically, almost all content is reproduced as faithfully as possible, but a few small changes had to be made: specifically they point out that some of the drop tables come from a mix of different early-WoW patch versions, and honour calculations now run while the game is live rather than during downtime.