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.
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.
War Mode: War Mode can be turned on at level 30 through your talent window, and will give you 10% bonus XP. You will, however, be attackable by players of the opposing faction, but changes have been made so that all players have a fair shot in a fight and even low-level players can kill much higher level players, and at least not get ganked and one shotted. Note: As of patch 8.1, you can get an additional call to arms bonus with war mode on if your faction is underepresented.
Within the context of Classic, the method most frequently proposed is to re-tune bosses to make them harder. Rather than copying the numbers, re-create the relative difficulty. Kind of like, when you first start working out, you use small weights. When you get stronger, you lift bigger weights. The WoW community is more knowledgeable, more experienced, has better hardware, etc. We're "stronger." So give us tougher bosses. There are a lot of forms that could take. Bosses were constantly re-tuned during vanilla anyway, so if Ragnaros does 10% more damage or something, is that really a problem? I don't think it is. What about resistance gear? back in the day, collecting resist gear was a thing people did. But the numbers and strategies are so well known today that only the tank really needs it anymore. Bosses could be re-tuned with more resistible elemental damage so that's important for entire raids to gear appropriately. That would be entirely keeping with the spirit of vanilla even if the actually numbers sitting in a database somewhere were different than they were ~13 years ago. If you want to go a little farther, a few people have proposed adding new abilities to old bosses, adjusting their timing, etc.
Even if you don’t have flying in WoD be sure to get the WoD handy notes. If you have flying simply fly and pick up all the treasures that you can and do bonus objectives. Not every single piece of treasure will be worth it though as some are hidden in caves or are just hard to get. So if you find yourself spending more than a few minutes finding a treasure, just skip it and move on, there is plenty of treasure to go around.