A quick double-question, Kerrick: are your opinions based on actual play, or are they just suppositions?
Okay, I'll have to admit that I've never seen one in use in PnP.. I've seen a couple in NWN PWs, but I don't know how those have worked out, balance-wise. So for a caster, it's probably not overpowered, due to the loss of spellcasting ability. For a mage/fighter, though, it's a huge benefit - take a couple levels in sorcerer, the rest in fighter or barbarian, and then go DD... I can say, though, that this class is horribly constructed, and I have to wonder how on earth it made it into the DMG.
First off: I've never much cared for the "if you're a sorcerer, then you've got draconic (or fey, or outsider, or whatever) blood", but I can ignore it for the most part, because it's not canon. Here we have a class constructed around that idea. All right... some sorcerers could have draconic blood. I'm cool with that. But... there's no explanation as to HOW, exactly, the PC is supposed to "use their magical power as a catalyst to ignite their dragon blood, realizing its fullest potential." Some suggestions would be nice here, as to how the PC could RP "unlocking his potential", like maybe an actual Special requirement.
Second: Whoever did this class didn't read the template very well. The half-dragon's HD is one higher than the base creature's racial HD. Humanoid racial HD is a d8, so it would be reasonable to make the HD for this class a d10. Also, half-dragons don't get blindsense, yet somehow they do through this class.
Third: For a class that's designed for a spellcaster, there sure isn't much here for them. Bonus spells?

Not only did someone invent a new mechanic, but it doesn't even make sense. Where are the cool draconic/spellcaster abilities? This thing is a transformational PrC, but that's all it does. It's uninspired at best. This could be a good PrC if there were additional abilities that made it worth taking - spellcaster levels, magic sense, or something tied to the innate magical ability sorcerers have - but right now, it's more geared toward fighters. Perhaps a clearer statement of the class' purpose would've helped the design here.
And finally: Either tone down the half-dragon template, or give the Dragon Disciple something less powerful. Drop the Strength bonus to +4, the energy immunity to resistance 20 (you're not a full dragon, you don't deserve immunity). ECL +3 is too much for a PrC. There's even an
epic progression for this thing on the Wizards site that grants the PC further transformation into a semi-dragon - breath weapon keeps getting more powerful, size increases, and you get a tail.
The reason I suggested bumping it out to 15 levels is that I think each +1 LA should be 5 levels. If you toned down the half-dragon, or granted the PC a lesser template, like the Dragon Devotee, you could make this a 10-tier easily.