This was not the first in the series, it was somewhere in the middle, I think, Aliens in London, Part 1. No spoilers here, just some impressions.
The production values are brilliant. The inside of the Tardis finally looks like a complex machine which may need to be hit with a rubber mallet to get it to cooperate. Vastly improved sets, lighting, special effects. Someone put some serious money into this series.
Casting is much more diverse. Blacks and East Indians in major supporting roles, the Brit version of white trash, etc. They forgot the senior citizens, though - everyone is under 40.
The writing is both better and worse. They make a constant effort to be current, but sometimes go a bit overboard. Campiness is part of the charm of the previous incarnations, and they have lost a chunk of that, I think. And without spoiling anything, I have to say that they should have left the farting out of this episode. It's a cheap laugh, and you would think they could come up with a more clever way to make the characters in question stand out. Sneezing, perhaps.
Billie Piper as Rose, the Doctor's sidekick, is excellent, but the role is seriously shallow as previous sidekicks go. Christopher Eccleston is not my idea of a Doctor. He's too normal. And they have written him as rude in a blatantly offensive way, where the traditional doctor is rude by being pre-occupied, absent-minded or maybe just out of your league. Noel Clarke as Rose's bloke Mickey is a gem. I want to see more of him, I want him to be a bigger part of the series. Frankly, if they had not blown it already by casting him in this role, I would have liked to see him as The Doctor. He could have pulled it off, I think.