Strong showing from House of Dragons episode 3.
I agree with most other commentators. That was a strong third episode of House of the Dragon! Hard to find much fault with it, really. They moved both characters and plot along, very effectively.
If there is a potential problem, it's that the showrunners are clearly invested in making Rhaenyra the main sympathetic character for the audience to root for. That could cause problems down the line, especially if they continue to stick fairly close to the book, plot-wise. But perhaps they will find a way around this issue.
If you have read the book, you know exactly what I'm talking about. If not, I won't try to ruin the plot, but will merely advise you to hold off on naming any kids after Rhaenyra at least until you've had a chance to see more (recall the people who named daughters after Daenerys during the run of Game of Thrones).
I thought the battle phase at the end was pretty nonsensical, even though it looked cool. I do not believe that Daemon’s forces would be “losing” a war against the crab people, given the info we have.
It seems like having the dragon blast fire into the cave while the other dragon burns all the archers would have wrapped things up pretty quickly. The crab people must be pretty clever to hide deep enough in the cave I guess, but then they foolishly all charged Daemon instead of shooting him with arrows while he was on the way to that central mound?
Also having the crab people headquarters be literally next door to Valeryon headquarters was dumb.