Today's crazy notion, and the logical steps leading to it:
1) Peter Capaldi, as just about everyone knows, was a huge Doctor Who fan long before he was cast in the part. He was, in fact, a Who fan from childhood who followed the series obsessively.
2) Andy Lane, in the Virgin New Adventures novel Original Sin, suggested that Time Lords could have more than thirteen incarnations--the real danger, according to this novel, is that after regenerating so many times, a Time Lord would have problems keeping his current personality separated from the memories of his previous personas, and would eventually degenerate into madness as he found himself shifting mentally from one incarnation to another. This would be even more dangerous for a Time Lord like the Doctor, who had such vivid personalities in each of his different lives.
3) Peter Capaldi has a killer Tom Baker incarnation, which he's actually cracked out on screen more than once (including "Mummy on the Orient Express", where he appears to be arguing with himself using his own voice and his Baker voice.
Postulate: Peter Capaldi, lifetime Doctor Who fan, read Lane's novel and the idea stuck with him. He's taken the idea on board in a slightly modified form and is playing a version of the Doctor who has a slightly looser grip on the various different versions of himself that are rattling around inside his brain--occasionally they get argumentative in a way that his predecessors didn't have to deal with, which is contributing to his somewhat crotchety nature. It's not quite as bad as Lane made it out to be, but the Capaldi Doctor is definitely having a little trouble with the voices in his head. And occasionally, out of his mouth.