I'm playing for the first time. I generally complete every quest before moving on to a new zone. I've found that as I neared completion of BC content on Outland, I'm close to level 80, while most of the sources online indicate that BC takes you from level 60-70. Am I an outlier or is this to be expected? Do people typically skip entire zones of content or complete only 60-70% of available quests?
World of Warcraft has always been designed so that you wouldn't have to visit every zone to progress.
This is most evident in the old world, both pre- and post-Cataclysm where you have several branching paths you could take. An example of this for Horde exists at level 10, where from Orgrimmar you can choose to go south-west into Northern Barrens or north into Azshara... or south from Undercity into Silverpine Forest.
In addition, Blizzard has dramatically increased how quickly you level at levels below 90*, meaning that you sometimes only need 1-2 zones per expansion to hit that expansion's level cap and move on to the next area.
*Note, it's 90 now because that's the lowest level for Warlords of Draenor, the newest expansion out at the time of this writing.
The quests are only one way of levelling: thus, Blizzard don't expect you to complete all the quests.
You can level via dungeons, quests, battlegrounds, etc. If it was the only way of levelling, they would expect you to finish main storyline quests (this is how it is for the current expansion always, so you can unlock things) but it's not. Quite a lot of quests aren't 'main' quests, either, so they don't really expect you to do everything.
Also, you get xp from killing monsters, doing professions, etc, all of which you do alongside questing. It can't be fine-tuned like that.
As Powerlord said, older expansion's levelling curves have been altered so you get to new content far faster. This means you don't have to do most things (I managed to hit 90 on an alt (questing, I normally level via dungeons) without leaving WotLK zones) to get to current content, or level cap.
Once you get to Draenor, you still have the options, but you are expected to do questing to get content, and levelling is far slower.