Lyte, here are some of my ideas. Please comment on them.
There is huge variance in player skill at the 1300-1500 elo level. I often get games where one or more players have absolutely no clue what they're doing. After the game is over, I look at their elo, which is the same as ours but he only has 16 wins. This kind of pairing ruins matchmaking and discounts experience as a factor in skill level. Plenty of people get lucky and shoot up in the short term.
Solution: Add a tier factor to each person's account, based on ranked wins. Hypothetically, let's have these tiers be 0-80, 80 - 180, and 180+. Matchmaking prioritizes putting together people who are in the same bracket, with some allowances being made if queue time takes too long. I believe this solves the inexperience problem quite neatly without negatively affecting anyone's gaming experience.
Duo queue pairs often have huge differences in elo, which either results in the higher level player rolling his lane and the game or the lower level layer's lane crumbling, leading to nonstop feed. This kind of scenario makes the game unfun for everyone and many of the games I play with duo queuers result in 20 minute surrenders on either side.
A secondary problem is the lower level player getting carried beyond his level. I've often a high level duoer whose partner is very new to ranked. This lower level player is often taught to play one role (support usually) reasonable competently, taught to play passive and hold their lane until his partner can snowball and win his lane for him. Once left alone, however, this lower lvl player becomes a real terror in his bracket, costing whichever team he's on the game due to his inexperience and inability to adapt.
Solution: Either pair duo queuers with similar elo differences against one another (possibly impractical due to limited availability) OR create an elo requirement for two people to duo (say, the lower player must be at least 85% of the higher players elo, to account for the fact that differences are less noticeable the higher you go). I proposed the second method because I'm of the camp of people that believe that the high difference pairs have no place in ranked. The matchmaking logic that 1000 elo players should not be paired against 1500 elo players should not change just because a 2000 elo player is along for the ride. Games should be full of 10 players whose elo level are approximately at the same level.