Just started to seriously play Daggerfall, and I think the levelling mechanic is broken on my copy.

Beat the Privateer's hold, and information on the web says that I should be ready for level two. Issue? I have no notification that I'm ready to level, nor where I am in advancing my skills.

Now, this is the second character to have done this (first one was short-lived.) Difficulty dagger is set to 0.3%, playing with the "Very fast" reflexes setting, and I pretty much killed everything in the Privateer's hold using Longblade (a primary skill) and occassional use of the Ebony dagger (minor skill) and some spells. Fast-travel and resting in an inn seems to have also increased a few skills, some of which I have chosen... but still no indication that I should be ready for level-up.

Am I just not getting it, or is my copy basically unplayable?

There are ONLY 6 skills that affect leveling up. The 3 Primary skills, the 2 HIGHEST Majors, and the 1 HIGHEST Minor.
2 of these (or 1 of them, twice) need to be increased in order to advance to level 2 (Subsequent level ups require 15 skill increases)
There is also a mandatory 6 hour interval between skill increases.

If these conditions have been met and you still can't level-up then yes, I would say that your game is messed up.

(Make sure it is your HIGHEST majors and minor that are increasing).

That... is a very counter-intuitive method for levelling.

6 hours before you can level up a skill? And how can you tell that a skill has been levelled up or is in the process of levelling up?

If you level up a skill, then yes, it will take 6 more hours before you can level up that, or any other, skill again.

There is no way to tell the progress of leveling up a skill.....although you could "save" and then rest for 6 hrs. to see if it is ready to level up (and then reload).

With the dagger at 0.3 I have found that you need to use a skill about half the number of times as your skill level. (e.g. If your skill level is 40, then 20 uses of that skill should be enough to level it up) A lower skill level, though, seems to require less uses. (i.e. A skill with a level of 20 might only require 5 or 6 uses to level it up). I would also think that the type of skill would have an affect, but can't say for sure.

It works.

Did a brief runthrough of the dagger all the way down, utilizing only short blade with a (what would be in later games called) stealth-specialist. Levelled up after recklessly travelling to Daggerfall.

My earlier issues must've been to be reckless travel. Odd, using my skills didn't seem to level them up, but using fast-travel did...