In my opinion, this is a bunch of opportunistic crud. If Romney is so sure his program can create jobs, he should be touting the program non-stop. However, his program, when you look at it, has a strong resemblance to Bush's program, and we all know how well that worked. So Romney has to focus on the meta-message (Obama is incompetent in economics) while avoiding a real message (here's my economic plan).
The Dems have perhaps started to get into this vibe too. Dems are asking, who accomplished more, Clinton or Obama? They're mostly saying it's Obama. I think this is a meta-message too: Obama will be like Clinton, as opposed to being like Carter. After a catastrophic midterm election, he'll bounce back, win re-election, and effectively govern for 4 more years.
The bad news for Dems is that Obama is not Bill Clinton. Clinton had a warmer personality and could connect with more moderate, middle-Americans. Obama has more appeal to the well-educated, but weak rapport with blue collar voters. The good news for Dems is that, unlike Carter, Obama is running against Romney, not Reagan. We don't know yet whether Obama will suffer Carter's fate or Clinton's.
As to the question of competence, I think it's reasonable to talk about it. Carter was an incompetent leader. Reagan was a very competent one. Obama is somewhere in between. We can't judge yet with Romney. So how will we make a decision? Best to use criteria other than competence, like WHAT ARE THEIR DAMN PLANS????