1) Well-established world, with continuity of story. This almost ensures a "strong" player base.
2) Movements and actions are fluid, and with the introduction of voiced dialogue it is easier to get immersed in the game.
3) Variants of the combat system dependent on class make each class feel atleast a little different, and they play differently. This is more than just cosmetic difference like in other notable games.
4) Easy to learn and get the hang of.
5) Fantastic compatibility between systems, OSs, and even notebook computers, which are notorious for not being able to run many MMOGs well.
1) Still "just another" MMORPG, offers virtually nothing new to the genre other than the game world -- which is still similar to that of other medieval/fantasy RPGs.
2) Cartoony graphics. However, this is a weakness to some while a strength to others. If you enjoyed the graphics and art style in previous Warcraft games then you will likely be very pleased with the graphic style in this game.
3) Another grind. Not a big deal if you're new to the genre, but the grind for WoW is unnecessarily long at lower levels due to long quests. Quests at early levels should not take so long to complete, and when they are dependent upon a large number of spawns in an area where EVERYONE will be hunting them... that's poor planning.
4) Small group size. The groups are not large enough to really get everyone in that you'd like, though nothing is stopping you from forming two groups and going out at the same time.
5) Player vs. Player combat seems and feels like an afterthought. It's just not that fun. This will likely be looked at soon after launch, as low levels don't engage in PvP much anyhow.
6) Lag. While not as laggy as most games on the market, WoW suffers from it at the worst possible times and sometimes for apparently no reason. Some players do not suffer from lag as much as others, and this could be due to ISP woes rather than server lag.
7) Chat interface unwieldy. The chat interface definitely leaves something to be desired.
Crafting has a lot of hunting and gathering. That's a personal peeve, not a mark against the game as a whole.
9) Un-specific quest logs. No continuous quest log.
10) Environment combat is unsatisfying at early levels, though it does pick up later to an extent.
11) Unfriendly start-up area. I say "unfriendly" because there's virtually no way to find out where to go, what to do, how to progress besides running around and talking to every NPC.
That's the short list. Read through it, some of what I consider weaknesses may be strengths to you.
Edited to add the 5th Strength.