Neil DeGrasse Tyson said himself that this is one of the most scientifically accurate movies. No obvious physics laws were violated, such as traveling faster than light. Wormholes and the Dyson sphere at the end are plausible even if impractical with modern understanding, and if nothing else this movie gets my vote for acknowledging time dilation, which I think is a first for movies. We can't really talk about the scenes in the black hole because we have no idea what could be possible in the extreme environments of a black hole.
Yes, I think the movie did a good job overall in adhering to real science. Nowadays people who make movies consult with teams of experts to get their facts right. There will always be some creative license in order to propel the story forward and enrapture audiences. There will always be some bending of the rules. But overall, the movie stays true to science.
Science advisers get a bad rap, as we blame them for the silly stuff the let through, but never hear about the even stupider stuff they manage to block.
For example the science adviser for The Core is often maligned for the abysmal science in that movie. He had spent long arguments prevent "Magma Space Suits" and a Windshield for their drill to the centre of the Earth.
Or Brian Cox, who was the science adviser for Sunshine. Thanks to him the movie was pretty realistic with it's depiction of space travel, apart from the premise of using a bomb to restart the sun.
When the directer has an idea in their head, it's very hard for the science adviser to stop it.
Who cares? Things happen in movies all the time that make no sense and couldn't possible happen. I suppose they did do a good job of trying to be somewhat realistic, but if they hadn't, I wouldn't have really cared. That's what movies are - flights of fantasy, things that may not otherwise be possible.
I think it is wonderful that Nolan listened to the scientist and tried to keep to the current theories on the impossibility of traveling faster than the speed of light. The tesseract idea, I think, came from a Wrinkle in Time. I was delighted to have a visual reference for a favorite childhood story.