So, let's look at all the things that are great about it:
For Horde players, getting to the Scarlet Monastery is extremely convenient, as it only requires a two-minute
For the Alliance it's very much the opposite and to be honest I'm not sure why the instance is so popular with them despite of it, but I guess it offers enough incentive to go there to make it worth it. As it is, an Alliance player who wants to kick some Scarlet behind has to fly to Southshore and then cross three zones on their own, one of which is enemy territory. Nowadays you can at least ride, maybe even already at 100% speed increase, but back when I played Alliance you usually had to walk all the way, which considerably increased the risk of getting ganked by a passing Brill guard. And yet people still did it en masse even back then. Go figure.
The Scarlet Monestary is very much not a dungeon in the classic sense, but it's definitely atmospheric. Even though the place isn't much to look at, it does look and feel like a monastery, with its sun-filled courtyards and quiet alcoves stuffed with bookshelves.
3. Story & Quests
The Scarlet Crusade doesn't have a story with a beginning and an end, but they are simply an entity that will be present as a common enemy throughout your whole levelling career. If you start as Forsaken, you'll encounter Scarlets as early as level three. They are all over the plaguelands and in Northrend you'll end up facing the Scarlet Onslaught, which is just a fancy name for "Scarlet dudes who went to Northrend". As such taking out some important characters belonging to this faction feels quite satisfying. Kelpsacovic would call them "well-crafted" I guess.
In terms of quests, there are quite a few connected to the Scarlet Monestary. Both factions have a quest to actually take out all the bosses except the ones from the graveyard, and most of the others are about finding books in the library. Makes perfect sense and adds a nice chunk of XP!
The Scarlet Monestary was the first instance to be split into different wings, four in this case: the graveyard, the library, the armoury and the cathedral. This was quite a stroke of genius as it meant that you can basically choose the length of your instance run. If you've got a lot of time on your hands you can clear all four wings in one go, but it's just as acceptable to stop after only one wing. Since they are all separate it's not like someone suddenly bailing halfway through BRD, leaving the party with the awkward question if anyone even remembers the way back to the summoning stone to get a replacement.
What this means is that the length of this instance is simply... ideal. It can be short, relatively long and anything in-between just as you require. If that isn't a great design then I don't know what is.
You'd be hard-pressed to get lost in any wing of the Scarlet Monestary as it's quite linear - either you go further in or you run back out. Fortunately that doesn't mean that it's just a boring tunnel, it still feels like a real place: The library has little alcoves with bookshelves and extra mobs inside for example, and the cathedral has a massive cloister with fountains, through which you can choose your own path at your leasure without having to kill off all the trash in it.
Speaking of trash... the Scarlets are actually reasonably challenging at level, mainly because almost without exception they will run away when they get low on health, making it very easy to get adds when you really don't need them. A lot of them are also able to heal, which makes getting adds even more annoying as you'll have to deal with multiple opponents healing each other up all the time. Some of them also have other annoying abilities like stuns and kicks.
On the plus side, if you've ever been annoyed by paladins' seeming invincibility in PvP, you can have a field day in here by killing them in droves. It's obviously not the same, but still satisfying.
The Scarlet Monestary has some very iconic and memorable bosses, the most important ones being Herod with his "blades of light" and Whitemane and Mograine. "Arise, my champion!" See? I'm really bad at remembering quotes but even I know these without having to look them up.
As far as difficulty goes, none of them are very hard, but you have to consider that this is a relatively low-level instance where people are still learning. Newbies to WoW at least get an early chance to familiarise themselves with some basic strategies like "moving away from spinny blades of death" (Herod) or the relevance of kill order (Whitemane and Mograine).
Loot from any levelling instance is obviously always going to be temporary, but some of the drops from the Scarlet Monestary are likely to last you for a long time. Whitemane's Chapeau is such an awesome caster hat that you might keep wearing it until Outland for example. Any drops from Arcanist Doan are going to make the clothies drool. Plate wearers that can't wear plate yet will be delighted by any piece of the Scarlet set. Ravager and Mograine's Might are lovely weapons for anyone who likes to smash face with a big two-hander (though the proc on Ravager gets a bit annoying after a while). And Loksey's Training Stick is one of the first instance drops you'll find that is specifically tailored towards hunters and feral druids. There is more of course, but these are some of the nicest and most common drops.
It's worth mentioning that an extra, max-level boss can be summoned on the graveyard during Hallow's End, the Headless Horseman. He's not hard to kill and drops lots of fun stuff, making the instance worth a visit for all