Occasionally it's also been proposed to re-randomize all the gear. We didn't have best in slot lists back then. People weren't starting out as a fresh level 1 character with a complete list of which dungeons to run at 60 in order to gear as quickly and efficiently as possible. Now, all that data is available. If gear were re-randomized then all of those lists would become useless and thing would be close to how they were. Which is a more important part of the "vanilla experience?" the fact that item X from boss Y has exactly Z stats on it, or the voyage of discovery? Personally I think that voyage is way more important. Do you remember how many points of which stat on the ring or whatever that Darkmaster Gandling drops? I don't. Would it kill your experience if the BiS for every class were in a different dungeon so people had to actually play to figure it out rather than simply consult a spreadsheet? I don't think it would. For that matter, it probably wouldn't be a bad idea to handle it intelligently so that the better gear is in later dungeons. I remember there because some weird cases where level 40ish gear was better than anything that dropped in level 60 dungeons.
With the Classic beta now out it seems every related article somehow manages to spark the eternal war of "Vanilla was the best WoW sucks now" and "lol nostalgia goggles, Vanilla sucked, enjoy your two weeks of Classic". I have to say, even though I understand the principles behind the battle and the reasons people behave and talk this way... I actually REALLY don't get it on a deeper level.
Other methods have been discussed. For example, mods could be crippled. DBM didn't exist back then, and the other boss that did that I don't remember the name of, didn't do as much back then as DBM does now. If our goal is to recreate the experience as it was, then obviously not having DBM would be a reasonable way to accomplish that. DBM simply existing, makes the game today easier than it was. So disallow it. Again, this is completely consistent with the spirit of vanilla. Remember one-button-decursing? That was nerfed. They crippled the capabilities of the modding API to disallow that because it made the game too easy. So what if they cripple it a little bit more to once again make the game less easy?
That's not to say that everyone has an unrealistic vision of what vanilla WoW was like. There were already plenty of people on the WoW Classic forums pointing out that perceived bugs are just recreations of the original game. And as noted before, a flaw to one player is a key component of the original positive experience to another. WoW Classic will surely please plenty of purists in spades. But this goes to show that it won't be for everyone who has fond memories of the game circa 2006.