The main thing I noticed about both of Carter's Oz books is how derivative they seem, especially of Ruth Plumly Thompson's work. Carter often apes Thompson's style, and sometimes takes ideas for places, items, and characters directly from Thompson and other earlier Oz authors. Both Tailor and Mountaineer feature communities of mud people, an idea Thompson used in The Royal Book of Oz (the Middlings), and to a lesser extent in The Yellow Knight of Oz (Marshland). Jandy the mountaineer and Koko the cook also come across a town on top of mountain with a ruler on a literal high horse, which bears more than a passing similarity to UpTown. Carter reuses some of the magic items from earlier books, like the Hurry-Cane, Es-Cape, and Grab Bag. I don't really mind these talismans being used again, but I sort of wish there had been some sort of acknowledgement, like a character saying, "Hey, I've seen something like this before," or something. Then there are the character names. Tailor had a Wumbo who wasn't the same as the Wonder Worker from The Gnome King of Oz, and Mountaineer continues this trend with Bob Up, Tip-Topper (although it seems to be a title instead of a name in this case), Hi-Jinks (admittedly spelled differently), and Muddle. Once again, this wouldn't be so much of a problem if there had been some indication that Carter realized he was recycling names.
Now that I've established the book is basically a Thompson pastiche, I have to say that it's a pretty good pastiche of Thompson's more light-hearted, fast-paced Oz stories. I think some people have the idea that Thompson's writing is ALWAYS light-hearted and silly, which I find to be unfair. The fact remains, however, that she was good at writing in that style, and Carter does a pretty good imitation of it, resulting in a story that's fun to read.
If I might add one other minor criticism, I sort of think the incident where Koko is almost forced into marrying Princess Tip Topsy perpetuates the stereotype that overweight men are jolly and pleasant, while overweight women are irritating. I'm probably reading too much into it, though.