Hard to say what Romney's biggest mistake was; he was running a campaign against a popular, charismatic incumbent with a strong campaign in a time of economic growth. Coming within 4 percent was an amazing result; anyone else would've lost by double-digits.
Obama had approval ratings in the negatives, it wasn't 2016.
RCP has Obama's approval at 50/47 on Election Day 2012, which isn't great but is definitely above-water and almost perfectly resembles the actual election result of 51/47. Obama's approval ratings were consistently positive from September 8, 2012, to May 29, 2013, inclusive.