Interesting article on that here
Looks like the shift is occuring during the last few years.
It's still not correct according to the major manuals of style.
"Hereâ(TM)s what the New York Times Manual* states at the entry president:
â âoeIt is President Lamm(without a given name) in a first reference to the current president of the United States. In later references President Lamm; the president; Mrâ¦.Lammâ
This style is seen in todayâ(TM)s New York Times, as in the example in this article:
The order of mention is this: âoeBarrack Obama, President Obama, Mr. Obamaââ¦..âPresident George Bush, Mr. Bushâ
As you see, though, the Times sometimes goes against its own rules, citing the first name, too, as in this example.
â President Barack Obama moved quickly on Wednesday to lay some touchstones for the âoemore responsible, more accountable governmentâ he has promised, ordering a salary freeze for senior White House staff, tightening rules on lobbyists and establishing what he said was a new standard of greater government openness. âoeHowever long we are keepers of the public trust, we should never forget that we are here as public servants,â Mr. Obama said at a swearing-in ceremony for staff members in the Eisenhower Executive Office Building.
So, in answer to your question, I think it is correct for the first mention of the president to be President (Barack) Obama, and for subsequent mention to be Mr. Obama.
The style may be different in different publications or in different situations. I like this particular style.
There is something else to be considered: you could leave out the honorific President or Mr., as well as the first name, and use only Obama. Some newspapers use this style. I find it jarring and rude in a newspaper, but in a personal letter, it would be acceptable.
But I'm not going to loose my cool over it.