With shows like that, you have to remember that specific elements are exaggerated or invented for dramatic effect, even if the tone of the show is accurate. With Klondike, I'll encourage you to read any of Pierre Berton's books on the Klondike. His stuff is older, but it's designed to be read by a general audience: It's an easy and fun read, and it has a good reputation for accuracy.

For a specific answer to you, I recommend reading what historian Michael Gates' said shortly after the miniseries' release:

"In Scott’s miniseries, the history gets in the way of the plot, so it is massaged and moulded to conform to a typical Hollywood production. After a while, I lost count of the anachronisms.

Guns and murder prevail. In one scene, Bill Haskell, the main character in Klondike, is trying to arrange for a funeral for his friend, Epstein, who was shot in cold blood on their claim. The undertaker, who has a pile of corpses to deal with, informs him that he is going to have to wait a few days for his turn.

At the height of the gold rush, not one murder was committed in Dawson City, and while there was crime, most of it was the white collar variety, perpetrated mainly in the corrupt government mining recorder’s office.

Jack London appears in the summer of 1897, and crosses paths with Haskell - months before he actually arrived in the Klondike. And while the real London spent most of his time in the tiny community at the mouth of the Stewart River, and then came down with a debilitating case of scurvy, the Hollywood version is healthy and robust, and hanging around Dawson City.

Father Judge was not on the Chilkoot Trail in 1897, he was in Dawson City, where he had been since he moved from the town of Forty Mile in the autumn of 1896. And the Mounted Police? Well in this version, they arrive the summer of 1897. In reality, they actually arrived in 1895, and had established British-style justice before the gold rush even started.

The Tr’ondek Hwech’in may not be happy with the portrayal of First Nations in this film. They have been replaced, or displaced, in the script, by the Tlingit people, who actually lived a thousand kilometres away in coastal Alaska. In the third episode, they attack Dawson City, killing a Mountie, after which the Mounties ride after them on their horses, dressed in red serge to hunt (and shoot) them down. This was a piece of absurd old-style cowboys and Indians Hollywood. It certainly never happened in the Yukon."