Obama has committed FAR less verbal gaffes than Bush, or even Palin. That's not really all that important, at least not from my perspective. But it's still a fact...
Certainly, the fact that the media in general tends to lean left does tend to give mistakes made by conservatives a little more airtime/press than mistakes made by liberals, but it's not the size of discrepancy that you seem to believe. You haven't seen people consistently making fun of Biden and his verbal miscues? Including such "liberal outlets" that you have repeatedly criticized as Saturday Night Live and the Daily Show? Obama doesn't get the heat for accidentally adding 10 states that Bush did for all the ridiculous things he said in the spur of the moment because, off the top of my head, he's made maybe 2 such mistakes. Bush made dozens. Palin made at least a dozen, probably dozens. So they get made fun of. If you do anything in the public eye you have to anticipate that. Goes with the territory. You'll likely get the same types of things from a guy like Chris Christie, because he likes to speak extemporaneously and doesn't always lean on the speechwriters as much as most other prominent politicians. Most Republicans and a number of Democrats really like that about him, but it does tend to lead to repeatably miscues. You don't get it from Romney, but he's boring as hell. Obama manages to come somewhere in between - not exciting, but much less boring than Mitt, and without a lot of mistakes. Reagan was the king of speaking, totally charismatic and often "felt" off the cuff, but he still didn't leave the quotable mistakes.
Anyway, long story short, it's not really the media, it's the reality of the fact that recent Republican leadership has said more stupid things than Obama or Gore or John Kerry.
Of course, Gore and Kerry fell into the Romney boring category...