Yes Tigh is a drunk, but there's a reason that Admiral Adama keeps him around. When the pressure is on, Tigh is a damn good XO! However, that's all he'll ever be. His downfall other than being a drunk is that he is not in touch with the average man. Much like a bad politician, he cannot relate to the average person. But in the military all you do is take and give commands, and Tigh does that well. As questioned in the film "A Bronx Tale" would you rather be feared or loved? Adama has the respect and love of his entire crew because not only can he give commands, but he knows how to listen to his crew.
Adama definitely did the right thing for the good of the fleet by promoting his only son as Commander of the Pegasus. After all that's happened lately on board the "Beast" and it's dead prior Commanders, he provided them with an individual that knows what the hell he's doing, and most importantly someone that he and President Laura Roslyn can trust. Especially with the popularity of Gaius Baltar on the rise amidst an election year.