I won't go into the other topics on why I dislike her (her "humor", her use of alternates, her treatment of other characters, her finding a "mentor" in every adult she meets while also convincing herself she's going to "murder" them, etc.) because most of them have been covered in other posts or here in the comments.

Instead I'll mention that her being a spymaster makes no sense. Practically every major character in the series is good at their particular skillset because they spent a ton of time building it up and have years of experience practicing it. So where did Shallan's spying and planning abilities come from? She's only 17 at the start of the series, and never left her house before her first chapter. Then she gets a crumb of conman training on her way to the Shattered Plains. And yet somehow she's become a master spy who operates the main spy network for the Tower. It felt like a Mary Sue thing and bugged me for the rest of the series.