Dudes Beating Down
Paladin decks have a plethora of good cards, and have been in and out of the tier 1 meta for the last year or so. With the decline of Priest decks, Paladin has once again risen to the top of the meta, lead primarily by the power of Call to Arms. This card creates a powerful board presence that is fueled by the combination of cheap, efficient minions who synergize well with one another. A Knife Juggler that survives long enough to be around for a Call to Arms, for example, should help push enough damage or clear board quickly enough to end games around turn 6 or 7.
Ideally, the mid-game is where you want to end. The deck can run out of power in the late-game, although Divine Favor can help refuel your hand efficiently versus slower decks. The Divine Shield minions plus Dire Wolf Alpha allow many of your early minions to trade profitably, as well.
Additionally, the two weapons in the deck are an essential inclusion, in my opinion, in maintaining the decks tempo and power. They synergize well with your go-wide minion strategy while allow your minions to push damage as you trade life total for board presence.
As far as matchups are concerned, most of the slower Druid or Priest decks are a breeze. They are simply too slow to interact with your various minions, and most of the Spiteful Summoner or Duskbreaker decks simply cannot compete. If they clear your board you can simply rebuild it with a Call to Arms or Divine Favor into a bunch of little beaters. Rogue and Mage matchups are also a cakewalk, as they lack to the efficient clear to answer what the aggro Paladin decks are doing. Most of the removal in Secret Mage, for example, is spot removal that costs more to cast than the minion it's killing.
Control Warlock, however, is a different story. Mortal Coil, Mistress of Mixtures, and Defiles are all a beating and makes the Warlock deck a tough matchup If they ever play big papa Voidlord the game is most certainly over. Aggro Paladin doesn't really want to go past turn 6 or 7, ideally. Having said this, I've won numerous games through multiple early Coils and Defiles. The resiliency of this deck is noteworthy considering it plays a bunch of junky 1 and 2 mana minions. However, as is often the case with good decks, the deck is worth more than the sum of its parts. The emergence of Spells Hunter in response to the deck might require some tuning as well, as various cards they play are a huge problem for Aggro Paladin (Unleash the Hounds, for example).
As for the mirrors, I think the versions playing a Vinecleaver and Steward of Darkshire are favored. They give you extra value on your 1/1s, and Cleaver goes over the top in the mirror match. The versions that play Cleaver also get to play Lightfused Stegadon, which can be great in the mirror or any grindier matchups. However, I've tried lists with and without it and both have performed well. Furthermore, I have tried versions of the deck with and without Equality, and I think the card is often unnecessary. I think the Sunkeeper Tarim is probably enough for what you want to be doing. The version I have been playing, shared here, is a bit tech'd out to beat some of the tougher matchups, but I'm still not sure about Spellbreaker. The card is often a 0 or a 10, and never really anything in between. There are matchups where it wins you the game on the spot, and others where it is a vanilla 4/3 for 4 mana that doesn't matter and is too overcosted for the matchup.
In any case, this deck has completely overrun the meta and the last while, and on ladder it is easy to see why. This is a deck that is conducive to climbing very quickly, as you win and lose games in very short order. Be careful to sequence correctly (if you have a weapon don't use the last durability before a Call to Arms because of Southsea Deckhand, etc) and the deck has a lot of power to it.
As for mulligans, you can keep most hands with early plays, but you don't need many. You can try to aggressively mulligan for a Call to Arms, as the chances you draw or mull into early plays are very high given the makeup of the deck. However, there are some unlucky times where you mull into hands like this: