The "Healing Montage" page in Chapter 3 where Tanica gave a 168-year-old lifelong geek a run for his money in a game of Go isn't just a throwaway gag — for all that she doesn't believe in herself, Tanica is actually really smart. (I mean, honestly, four college degrees? And in a lot of practical majors — chemistry, economics, and engineering majors particularly — graduating with a low GPA is common.)
Another note on Tanica/Elka: for the longest time, I assumed that Elka assumed the name "Tanica" because the Trsanti wanted her to separate her new identity from her previous one. However, as is noted under Meaningful Rename, the Trsanti don't require any change of name — Lulu was Lulu to her mom and to her boss. Given what we know about Elka, she has a lot of reasons to change her name when she becomes a Trsanti, not the least of which is she saw "Elka" as a failure, so changing her name to "Tanica" gave her a chance to not be a failure. This doesn't just make her comment on murderers being failures more meaningful; this underlines the way in which her changing the name back represents a That Man Is Dead attitude towards her career in the Trsanti.
It's been mentioned that Goro did surgery on a dragon, but it hit me that very well could have been the first (or among the first) patients that the team did. The Dragon Doctors are called The Dragon Doctors because they literally were doctors for at least one dragon.
If you notice, Jack Coral doesn't show up in Blue's company until Chapter 9 — several weeks after the Dragon Doctors end the valley curse and settle in Tinto — with his own car and no job. In other words, he shows up in town as quickly — and with as little preparation for his future needs — as you would expect from someone who knew that Cary stole a harvest stone, knew that (s)he tormented his mother in the process, and saw a report of a harvest stone in Agri Valley in the news.