This deck looks like it wants to be two things at once - a Divine Spirit/Inner Fire combo deck and a Spell Damage burst deck. I would pick one of those directions and stick with it. I wouldn't expect going halfway on each direction to work very well.
Much of the time Divine Spirits will be dead draws in this deck because there are almost no minions to combo with them - Light Spawns, Yetis, etc. Even when they do combo, you might have problems. The lack of minions also makes Northshire Clerics next to useless (notice that Dragon Priest doesn't play them at all!)
But Inner Fire is pretty unreliable, and more so in this deck, because it's mostly a non-minion deck.
Let's say you get 2/3s of The Dream - Gurubashi + Inner Fire and you make a 7/7 on turn six.
Well you could get most of that, all the time, with an Ogre, and the Gurubashi damage effect doesn't really do much in that case (if your opponent trades two minions in to kill it, they're both going to die anyway to a 7/7 (or a 6/7) and the fact that the second minion hits a 9/3 or 9/4 rather than a 7/3 or 7/4 doesn't really do much.)
So I would drop the Inner Fire stuff as an unreliable finisher.
What makes the expensive Dragon Priest really tick is that Prophet Velen/Malygos/Alextstraza/Ragnaros either magnify the effects of your burst damage or take the opponent's health right down so that the burst is effectively magnified. I've never played it - who has the money? - but I suspect the burst damage in your deck is effectively halved from the full deck.
The whole strategy of the Dragon Priest is to get to late game while removing everything the opponent throws at you and then dropping the big guys. If the big guys aren't there, there are problems :-)
The budget version, though, just lacks most of the punch. If you draw all your major burst, I would count on 15 points of damage - but where is the other 15 points of damage going to come from?
Because a big part of the spell damage deck is keeping the board clear against aggro, I would add in Wild Pyromancers as quickly as possible - they are a great board clear when used with Power Word: Shield or Holy Smite. I would also add the second Holy Smite immediately - why only run one in a spell damage deck? (Pyros are well worth crafting anyway, since they are generally useful in many different decks)
The second Azure Drake will also make this deck a lot better.
I would drop the Mind Visions - unlike ThoughtSteal, which actually gains cards, Mind Vision is a gimmick card, and there is no reason to believe that a card from your opponents deck will perform better than a card you pick which is tailored to fit your deck's strategy.
I get that you're using the Kobold Geomancer as a replacement for Thalnos, but I would drop it, because a big part of the allure of Thalnos is that he has no downside - if he's a dead card in your hand, you simply cycle him for two mana. If the Kobold is a dead card, you're stuck with him :-) The spell damage isn't worth it for the card slot, even in this deck.
Also I would drop Mass Dispel. It's probably good against Miracle Rogue, but otherwise I don't think it pays for itself.
I would drop the shadowform, because you only have one, and it has total anti-synergy with the Northshires. Either it or the Northshires should go, and I would rather keep northshires and add some healable minions.
So I would drop 10 cards -
2x Mind Vision
1x Inner Fire
2x Divine Spirit
1x Kobold Geomancer
1x Mass Dispel
I would add
1 more Holy Smite
2x Wild Pyro (as a priority)
2x Yeti (because Yeti is ridiculously good in a priest deck)
1x Azure Drake
2x Temple Enforcers (if you have them, Ogres if you don't)
2x Argent Commanders (if you have them/can afford them, otherwise Rocketeers)
My plan with these additions would be to have some tough minions to play that hopefully stick around long enough to put in damage on the enemy hero, before final burst takes him down.