I try never to judge a show based on its first episode, because there are so many kinks to get out, and it takes a while to discover your voice and pace and structure, but I thought it went reasonably well. I quite like him bringing all the guests out at once, though viewers of The Graham Norton Show on BBC America will no doubt recognize that from Norton's show. It works wonderfully with Norton, so it could here, too. The difference is that the BBC show is once a week, so they always fill the sofa with lots of top stars, at least three and often four. That works well for lively conversation. I'm not sure yet how it will work on a nightly basis, without the same level of star power, and only perhaps two guests. Still, I like the effort and that Corden brought his chair to the front of his desk. Though a) that's where Graham Norton's chair is, too (though a bit farther away...), and b) if your chair is going to be in front of the desk...why have the desk? There are a few times it was nice to have, but not necessary.
On the negative side, they have a really terrible opening theme song, whose lyrics, if I remember correctly, are something like "This is the Late, Late Show. The Late, Late Show. It's the Late, Late Show. This is the Late, Late Show. This is the Late, Late Show." And thev'e got to figure out to how better use the band leader/announcer. I'm sure that rapport will work out in time.
They had a couple very good video pieces, one of which was a particularly joyous sketch with Tom Hanks, recapping the actor's career in seven minutes. Both men were great in it, and Hanks (for obvious reasons) seemed to have great fun -- most especially in the Toy Story part, where he got to play his cartoon character. And did so, as if he was a cartoon character. It was also very smart of Corden to do the sketch, since it showed off his talents, as well, to an audience that largely doesn't know him.
If you didn't see it, here it is. And if you did see, I suspect you'll love seeing it again. (And forget the title of the video, it's not eight minutes. As you can see below, the video run 6:55. It's sort of hard to miss...)
I also liked the song they had at the end. It had a nice combination of touching and funny lyrics, but again was very smart to do, since it too showed off James Corden's talents and made clear he's quite a good singer. (As was likely clear to anyone who saw him in the recent film musical, Into the Woods.