Here comes the first stress test for the Classic beta, and Blizzard will be inviting a lot more people this time around. It's taking place this Wednesday, May 22nd and will last for 2 hours from 4-6pm PDT, but the realm itself will be available for a full day. All races and classes will be available, but the max level will be set to 5. Also, current beta testers will not be able to play their beta, but will have to join the new stress realm and make new characters if they want to play. 

The fact that Cookie's Tenderizer from the Deadmines had +3 instead of +2 strength. The fact that the Stormwind south bank had one instead of two mailboxes. The fact that Jaina's Proudmore's name was "Jaina Proudmore" instead of "Jaina Proudless." Stuff like this isn't what mattered. It was arbitrary. If Cookie had dropped a shield instead of a mace and Jaina had been named Susan, nobody would have cared. It wasn't specific details like these that caused us to enjoy the game.
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?
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.