As fun as the PvP in Warhammer Online is, I found that the sub-par PvE eventually killed the game for me. After having had some time to reflect, here are the three biggest issues I had and what I believe could be done to address them.
No sense of "place" (immersion)
The PvE zones provide very little sense of "place." They seem designed mainly with utility in mind rather than to immerse you in a virtual world. The fact that you can quest by running from red blob to red blob on your map, reading nary a bit of quest text, further reinforces this impression. The zones are laid out as a means to an end, and that end is guiding you through quest grinds so that you can level and get back to the PvP. Zones are simply a means of guiding your progression in nearly any MMO. However, this is masked much more poorly in WAR than in an average MMO.
How to fix it: Unfortunately, the zones are in place and it's really too late to fix this. A few things could help. One simple change would be to further encourage exploration. There are a lot of little secrets in each zone that exist for no other reason than unlock entries in your Book of Knowledge. Perhaps this system could be incentivised? Giving users the option to turn off the "quest blobs" might also help some players with immersion. Of course, the quests would have to be clear enough that you could find objectives based on the text for this to work (see below).
Mob density and respawn rates are too high
It is a serious pain in the butt to get anywhere in the PvE areas. When you are sent into an enemy area for a quest objective, you will be killing something nearly every step of the way. And when you get there, everything will have respawned behind you. If your swift travel isn't up or is set at a useless place, prepare to kill everything again. It makes the entire experience of questing incredibly tedious. This more than anything killed the PvE for me.
How to fix it: Lower respawn rates in areas outside of public quest zones. Lower the mob density to the point that you can expect to fight 2 or 3 adds getting to an objective (like most MMOs) rather than dozens.
Quest text is sub-par
I am a huge fan of lore in MMOs. I am one of those anal types that will hold up a party so I can read every bit of quest text in a chained group quest. Not so in Warhammer online. Save for the Greenskin quests most of the quests in WAR read like "bla, bla, bla...go kill some lizards" (or whatever). This is odd because the writing in the BoK is excellent. About the only part of the PvE I consistently enjoyed was unlocking new entries. The prose in many of the Greenskin quests is also excellent. There are obviously some good writers at Mythic.
Unfortunately, most of the quest text reads like a first or second draft. The prose is tends to be inefficient, and conveys little sense of the personality of the quest giver. The quest instructions are also generally vague. Without the red blobs on my map I doubt I could have found most quest objectives.
How to fix it: Pay whoever wrote the entries in the BoK to go through each zone streamlining and clarifying the quest text. Decide on what mood to convey in each zone, and make certain that every quest contributes to that goal. Either by reinforcing the mood, or by providing notable (and infrequent) exceptions to it. Rule of Thumb: any quest text much over two short paragraphs better be conveying one hell of a story, or you will lose your reader.
You may have noticed I said nothing about the PQ system. Mythic does seem to be aware of the current issues with them, and so I don't think much more needs to be said on the subject. And when you have enough players to get through a PQ, they are arguably brilliant.