A bit of a pet peeve of mine, I've seen a lot of fanfics where Sesshoumaru's way of referring to himself in third person is either corrected as being improper by Kagome or treated as a yokai speech pattern. The way he talks is actually an old way a high ranking person would talk- so completely correct for a feudal lord. Because its considered formal speech, he should drop it when speaking to someone he is close to.
Just wanted to put this info out there!

I agree with your statement, for the most part. I also think it depends on the setting for the story.

If it's more inclined to modern AUs, then it would feel stilted if he were to talk and refer to himself in the third person. Though this could work if the situation were a serious one with him dealing with some sort of council or characters older than himself and thus very traditional. But, if the modern AU has it where there are no youkai/demons (however you wish to call them personally) and everyone is simply human, then this would feel very out of place and making me question his mental state in the story in question.

Now, if we're talking canon divergent, then yes. It tends to throw me off when I'm reading a fic that takes place in the past and the only exposure that he's had to anything modern would be through Kagome, but all of a sudden he's speaking like a modern native. On the one hand, I understand that writing speech in something more traditional and fleshed out can be a challenge if the writer isn't used to it, especially since everything about language has evolved and shortened for quicker communication. On the other hand, when it's due to pure laziness, I'm more inclined to abandon the story altogether than give it a chance.