There were some silly aspects, but I happened to enjoy weapon skills. That might have something to do with playing a Warrior and being able to rank up everything except wands and getting into shits-and-giggles Unarmed sparring contests with my buddy though. It was a persistent progression I liked.
As for attunements weeeeeeeellllllll....I did like needing to complete quest for entry requirements, but the early ones were brutal. I forked out the attunement mats for like, 30 people to enter classic Naxx (on my own, mind you), and that's not particularly an experience I liked. Furthermore, the lack of LFG system meant that asking around on chat for hours to get a group was also mean, but in retrospect I don't mind it as much as the distinct lack of communication there appears to be now.
Burning Crusade was my favourite version of the game, and whilst I would say that elements of the game (i,e: the quests) have distinctly improved with some of the later expansions, a lot of stuff that I did enjoy has been taken away. The idea of releasing raid gear after 3 months to something as braindead as Heroics in Wrath had me thinking, "Why the fuck do I bother?"
Furthermore, the changes to classes and talents are definitely something I don't enjoy. They are a lot more homogenous and alike than they used to be, the differences only really come from the way they approach their archetype (tank, DPS, heals, etc.). I vastly preferred the big talent-spending trees of old, and Paladins were kickass when they had a whole Blessing/Seal/Judgment system where different combinations all had different effects.
So I do miss old WoW and the intrigue and fun that came with it. I'll take playing that version over one where the newest feature is a half-baked Garrison where you can send your minions off to cheap Facebook battles.