This is an update post.
These days instances before Northrend have become quite unpopular, no doubt due to the fact that most players are geared in Bind on Account items which are as good as the loot you're going to find in an instance. However, as I don't have a level 80 sponsor, I have made an effort to join some instance groups while I level, and have on occasion had the opportunity to run one.
Finding a full group, and keeping them together until you actually get into the instance is the first big challenge. Once inside there are a few more challenges.
- I assume most of these players are alts, yet no-one seems to have a clue about group "roles". Only after the first wipe does someone pipe up with the idea "okay, who's tanking? And who's healing?". I actually had our druid healer say, after a wipe in Stockades "I was DPSing that fight". You can't just switch roles throughout the instance!
- I quickly got the impression that rogues have a terrible reputation in groups. Every time there was an accidental pull, or some kind of mess up, people assumed it was me. Fortunately I had people in the group own up to their mistakes, but did get a little irritated by always being blamed for anything that went wrong. Eventually I just got tired of defending myself and just became the martyr for everyone's screw ups. Oh, someone pulled the boss? Must have been the rogue. "Yeah, it was me".
- Other than Deadmines and Stockades it feels like Alliance have to pass through dominant Horde territories to get to most instances. Wailing Caverns is in the center of the Barrens. As is Razorfen. Blackfathom Depths is along a coast which is a major Horde quest hub. Shadowfang Keep is way out of the way, but even still not as bad as Scarlet Monastery. Most players expect to be summoned because getting to any of these instances usually requires going way out of your way, traveling long distances, and usually getting ganked a few times during the trip.
Here's a screencap of one of my better groups. We actually finished the instance. That doesn't happen often.

The best instance I did was Gnomeregan, where my brother ran me through it on his priest. I assume this is how anyone gets through an instance these days because its just too much trouble to do it the authentic way.

PS: Just wanted to give a shout-out to my friend Kordwar. Congrats on all your recent success in arena, bro! I miss hanging with you.
Samyon out!