After several years I've read the novel for the first time (and the first time since I've seen the show) again btw.
Overall, they made pretty good use of the source material. While Season 1 serves a direct adaptation of the novel, even Season 2 features sections from the book, most notably the episode with the prayvaganza where Gilead soldiers get married to child brides. Sometimes even throwaway lines from the novel made it into the show somehow. For instance, it's mentioned at one point that Canada didn't want to enrage its powerful neighbour to the south and extradited runaway handmaids back to Gilead. As I recall, that's exactly one the things the Waterfords' diplomatic visit to Canada was about in the show, even though Gilead's attempt at getting refugees extradited by the Canadian government ultimately failed in the TV version.
For me, the most glaring deviation from the book (aside from the more well-known ones like the Waterfords being siginificantly younger on TV than in the book, Gilead not being a racially segregated Apartheid-like society any longer, and the existence of a rump U.S. government headquartered at Anchorage which had been completely absent from the novel) is a more three-dimensional depiction of the character of the Commander.
While the Joseph Fiennes version is often depicted as a downright vicious asshole, the Commander from the novel comes across as generally well-meaning, albeit in a warped, excessively paternalistic sense. He likes to thinks of himself as the good guy, and sometimes seems to exhibit genuine ignorance and naivity with regards how badly people and especially women have to suffer under the regime he helped to create. For instance, the Commander from the novel doesn't really strike me as the kind of guy who would personally order the amputation of his wife's finger. He'd probably find a reason to excuse her behavior, while conveniently ignoring the fact that such things happen all the time in Gilead in his absence. But that's just the thing: Not having to deal with any real atrocities first hand probably makes it easier for him to authorize them for others in the book.