Took the Crusader, ended up getting a third murloc knight. Will probably tank this because of my glut of 4 drops.

Bloodsail Corsair
Boneguard Lieutenant
Frostwolf Grunt
Micro Machine
Puddlestomper
Snowchugger
Sorcerer's Apprentice
2x Stonesplinter Trogg
Ice Barrier
Harvest Golem
Imp Master
Spellslinger
Spider Tank
2x Cone of Cold
4x Fireball
Arcane Nullifier X-21
Goblin Blastmage
Kvaldir Raider
Silver Hand Knight
Priestess of Elune
Sunwalker
Captured Jormungar
Gruul
2x Frost Giant

And it largely failed because my stuff traded at worse than 1-for-1 with enemy cards.

Bloodsail Corsair => I'd probably pick 90% of cards over this. It's terrible body isn't worth the tech against weapons. It's only redeeming factor really is that it is a one drop, but still not one that can apply any real pressure or trade with two drops.
Frostwolf Grunt => This card is very weak as it gets straight up eaten by ~40% of frequently played two drop commons. A two drop needs to be able to push for board control early as the value of two drops diminishes in the late game. It's a taunt, but not one that is going to get you any value and is easily destroyed.
Ice Barrier => Awful card, probably worse than 95% of picks. The problem with life gain is that it doesn't get you anywhere on board so you generally just fall even further behind and end up retaking even more damage than you healed. It's hard to make pure hero lifegain like this work in arena.
2x Cone of Cold => It's not a terrible card. One is pretty decent utility in most decks, but you rarely ever would want two and you might not even want the first depending on what the other two cards are. Definitely gets better in both hyper aggressive decks and decks with spell damage and area of effect spells, neither of which yours is.
Arcane Nullifier X-21 => It isn't awful but it isn't good or even average either. It is a Mech but probably not worth it even for the Blastmage. Since you don't have any other four drops that makes this better, but picking up better four drops like Yeti's would have been the even better option if it were presented.
Priestess of Elune => Same problem as Ice Barrier but at least this comes with a body. Still would pick most cards in the game over it as it has terrrible stats for a late game body.
Captured Jormungar => Passable if you need a late game threat, but you already have some good late game cards.
2x Frost Giant => Decent finisher for a class with a solid hero power, which the mage is. I wouldn't want two though.

Boneguard Lieutenant => This is a better-than-average two drop in my opinion. Mage's hero power is good which raises the quality of inspire cards slightly. And at worst it is a vanilla 3/2, which is at least reasonable.
Micro Machine => I'd say this card is worse than your average two drop because it is a 2/2 when you pass the turn. However it's upside is much higher than Grunt's and your Blastmage probably pushes it to being an above average two drop.
Puddlestomper => Mediocre, but definitely solid filler if you are light on twos.
Snowchugger => High quality two drop. Has the solid 2/3 body with an ability that makes it very strong against weapon classes and makes it relevant when it is outclassed on board. The fact that you have Blastmage makes this a great card in your deck.
Sorcerer's Apprentice => If you have 0 spells this is a mediocre pick, if you have ~10 spells it is fantastic. I'd say it's a "good" card in your deck.
2x Stonesplinter Trogg => I'd value this guy between Puddlestomper and Boneguard. He's kinda filler but (very) slightly better than a vanilla.
Harvest Golem => A great three drop, better than most. Fantastic pick considering you have a Blastmage.
Imp Master => Better than a lot of three drops, generally a good pick.
Spellslinger => 3/4s are really good since they don't trade with 3/2s, and the effect is good since you can play it as a potential out to basically anything as well as play it when you run out of cards.
Spider Tank => Really great three drop for the same reasons as Golem and Slinger.
4x Fireball => Hard to draft too many of these. The utility of threatening lethal from high amounts of health and being able to remove most creatures in the game is too good to pass up.
Goblin Blastmage => At it's worst it is a Lost Tallstrider which is kind mediocre but passable. Since your deck has five mechs I'd probably rate this as a great pick, if you had seven it would be fantastic.
Kvaldir Raider => A solid finisher, can win you the game singlehandedly if your opponent doesn't deal with it the turn after you drop it on turn seven.
Silver Hand Knight => A very solid five drop, good stats for the mana and the utility of two bodies. Better than Kvaldir as it's actually a really good turn five play, where Kvaldir is only a decent turn seven play if you can't protect it.
Sunwalker => Very solid six drop, not really a finisher but it can completely swing a board state.
Gruul => Very similar in role to Kvaldir Raider. It's hard to say which is better.

Shaman - Mage - Warrior (Choice: Mage)

Pick 1: Blizzard over Jeeves and Madder Bomber
Pick 2: Dragon's Breath over Ice Lance and Frostwolf Warlord
Pick 3: Zombie Chow over Undertaker and Antique Healbot
Pick 4: Cult Master over Dragonkin Sorcerer and Novice Engineer
Pick 5: Mukla's Champion over Faerie Dragon and Frigid Snobold (This one HURT. I really wanted that faerie dragon but Mukla's can just steal games)
Pick 6: Mirror Image over Southsea Deckhand and Reckless Rocketeer
Pick 7: Mind Control Tech over Young Priestess and Light's Champion (I strongly considered the champ...)
Pick 8: Acolyte of Pain over Mechwarper and Corehound (yeah, mech mage is a thing, but acolyte is so much CA.)
Pick 9: Micro Machine over Tournament Attendee and Kobold Geomancer
Pick 10: Ethereal Arcanist over Fencing Coach and Murloc Tidecaller (Terrible for a set of rares)
Pick 11: Senjin Shieldmasta over Lost Tallstrider and Mirror Entity (hurts to lose Mirror Entity)
Pick 12: Mirror Entity over Blackwing Technician and Frost Nova (I am rewarded!)
Pick 13: Cone of Cold over Dragonkin Sorcerer and Youthful Brewmaster
Pick 14: Mechanical Yeti over North Sea Kraken and Arcane Explosion
Pick 15: Ogre Brute over Flying Machine and Tournament Medic
Pick 16: Polymorph over Mirror Image and Annoy-o-tron (Ouch!)
Pick 17: Puddlestomper over Argent Horserider and Zombie Chow
Pick 18: Harvest Golem over Nerub'ar Weblord and Undertaker
Pick 19: Frostwolf Warlord over Dalaran Mage and Dread Corsair
Pick 20: Flamewaker over Mind Control Tech and Polymorph: Boar (Kinda wanted the second tech)
Pick 21: Salty Dog over Dalaran Mage and Antique Healbot
Pick 22: Water Elemental over Stormwind Champion and Novice Engineer
Pick 23: Arcane Intellect over Mirror Image and Frost Nova
Pick 24: Frost Elemental over Captured Jormungar and Southsea Deckhand
Pick 25: Arcane Explosion over Blackwing Technician and Reckless Rocketeer
Pick 26: Spectral Knight over Shattered Sun Cleric and Wisp
Pick 27: Lance Carrier over Reckless Rocketeer and Magma Rager
Pick 28: Spellbreaker over Spider Tank (ow) and Flame Juggler
Pick 29: Mirror Image over Youthful Brewmaster and Razorfen Hunter
Pick 30: Mogor's Champion over Pint-sized summoner and Secretkeeper

P2: I think your pick is defendable since it works better in a diverse amount of deck archetypes, but Dragon's Breath is one of the weakest Mage removals, so I'd probably go with the Frostwolf Warlord and hope to draft a more aggroish deck.
P5: I would have definitely taken the Faerie Dragon. Both Cult Master and Mukla's Champion work well in the same types of decks, but both require a low curve to function optimally. And well Cult Master is usually somewhat playable in any deck, Mukla's champion is pretty bad outside of a low curve deck or a mid curve Pally/Shaman deck.
P7: I think you definitely made the right choice. Mind Control Tech can completely turn games, and it isn't uncommon for people to try to rush Mage down before turn seven.
P8: I would have gone Mechwarper, but that's just a personal preference thing. I really like mech decks in arena.
P10: They are all awful, but Fencing Coach is definitely the least aweful except on the off chance that you get like two playable secrets. I'd say most Mage secrets are bad in arena though unless you have a Mad Scientist, so you really don't want to force yourself into a position where you pick them.
P11: I think this one is pretty close. After your last pick I might have gone with the Mirror Entity because it's more fun.
P13: You should go with Youthful Brewmaster here, half way through the draft it would be bad to only have 1 two drop.
P14: North Sea Kraken is one of the best neutral commons in the game, I'd highly recommend that.
P17: Zombie Chow is a much better choice here. Basically the same body power as Puddlestomper but for only ONE mana, has great synergy with Cult Master and Mukla's.
P22: Water Elemental is definitely the better card in my opinion, and if you'd taken the Kraken earlier I probably would have taken it. However at this point you have zero late game threats, so I'd probably have taken the Stormwind Champion since you are already over 2/3 of the way through the draft.
P24: Hard between the Frost Elemental and the Captured Jormungar. Frost Elemental is better, but if you take it the biggest butt in your deck is going to five toughness.
P28: I think Flame Juggler is the only defensible choice here. Juggler and Spider Tank are both amazing in their slot, but you are really lacking in two drops and have plenty of three drops. Spellbreaker is probably the weakest of the cards in your deck, though it might still be a better pick then the Tank for your curve.
P29: Definitely should have picked Youthful Brewmaster, you need two drops. Images are actually really bad in your current deck because you have nothing to back them up. They need to be protecting something.
P30: All of these are terrible, but you should have taken Pint-Sized Summoner because it is a two drop. You really don't need another Salty Dog, and Mogor's is even worse.

Blizzard
Frostwolf Warlord
Zombie Chow
Cult Master
Faerie Dragon
Mirror Image
Mind Control Tech
Mechwarper
Micro Machine
Fencing Coach
Senjin Shieldmasta
Blackwing Technician
Dragonkin Sorcerer
North Sea Kraken (Though I'd highly consider Mech Yeti because I have a Mechwarper)
Ogre Brute
Polymorph
Zombie Chow
Harvest Golem
Frostwolf Warlord
Polymorph: Boar
Salty Dog
Water Elemental
Arcane Intellect
Frost Elemental
Blackwing Technician
Shattered Sun Cleric
Lance Carrier
Flame Juggler
Youthful Brewmaster
Pint-sized summoner