(Note: I'm not a historian, but I've studied Norse mythology as a hobbyist.)

Gaiman's book is a retelling and deliberate modernization of the stories, and its primary purpose is to make the stories available and enjoyable to a modern audience. Toward this end, he doesn't change the essential details of the stories, but the exact telling and dialogue is his own invention.

For the most part, Gaiman's retelling is very conservative with content, and he is most inventive with the dialogue. Compare a portion of the story of the forging of Mjolnir, from the Skáldskaparmál, which is section XXXV in the version I've linked to:

Why is gold called Sif's Hair? Loki Laufeyarson, for mischief's sake, cut off all Sif's hair. But when Thor learned of this, he seized Loki, and would have broken every bone in him, had he not sworn to get the Black Elves to make Sif hair of gold, such that it would grow like other hair.

The beginning of the story is roughly 3 sentences. In Gaiman's text, this quote is spun into 3 pages (51-53), of which I'll quote a small bit:

She looked at Thor, horrified. "My hair," was all she said. Thor nodded. "It's gone," he said. "he has left you bald." "He?" asked Sif. Thor said nothing. He strapped on his belt of power, Megingjord, which doubled his enormous strength. "Loki," he said. "Loki has done this."

This passage does a number of helpful things for the reader: it establishes Thor's terse and impulsive nature, introduces his attitude toward Loki, and sets the scope of the story (Loki stole Sif's hair, and Thor is looking for restitution). Nothing that Gaiman writes here is a quote, but neither is it contradictory to anything in the edda. You can read the two stories side by side to get an idea of how much more he adapts the skeletal framework of the Edda story into a modern short story.

Where Gaiman adds detail, he does it to give the reader context that you wouldn't have without reading much larger swaths of the Eddas. He consolidates details from a sprawling record into a punchier story (e.g. naming Megingjord in the same story despite it barely being mentioned in the Eddas, he adds it for characterization rather than as a significant plot point).

He does carefully include details from the original; the line where Thor "would have broken every bone in him" is explicitly spun into a short conversation:

...if you do not put her hair back right now, I am going to break every single bone in your body. Each and every one of them. And if her hair does not grow properly, I will come back and break every bone in your body again. And again. If I do it every day, I'll soon get really good at it...

But while Gaiman invents specific dialogue to conform to the modern reader's expectations about story structure, he does not invent plot points or characters that are not explicitly part of the originals. He tells a very small number of stories from a very large collection of poems and tales, and cross-references a few details to give a more evocative view of some of the characters (e.g. opening the story I mentioned above with a paragraph summarizing how Sif is depicted and described).

There's a very good review at the Atlantic that unpacks how Gaiman structures his version and what a modern retelling means of the original Eddas, which themselves are post-Christianization records of many old stories.

In short, Gaiman's stories are 'accurate' insofar as they do not alter the essential content of the stories, but comparing his to the Eddas reveals a great deal about the differences in narrative expectations and the purpose of recording and telling stories.

As a follow up question, how accurate was Roger Lancelyn Green's telling of the same myths?

For anyone not familiar​, Lancelyn Green was a contemporary of C.S.Lewis and Tolkein at Oxford, and wrote a series of children's books in the 50s/60s - retelling the myths of ancient Rome, Egypt, Greece, the Norse, as well as Robin Hood, King Arthur etc..

I read them all as a kid, but never really stopped to check any of them later in life