Agreed about Rose's jealousy.
On Rose and Mickey get along really well - it felt a bit too quick after her pouting at the end of last time. Given what I remember happening over the course of the remaining episodes, they should have done a bit more to cement Mickey's place on the team, rather than it feeling like he's just there for a little bit. That Cleopatra episode sounds like it would make a nice story of its own.
Doctor as the "Romantic Hero" does work well. On the actual romance itself, I tried to ignore the whole "I met you as a 10-year old just as many minutes ago".
This was a very creepy episode, and as a standalone sci fi fantasy horror piece it works well. But it doesn't feel trek. Here's my conspiracy: With the dramatic different in tone, direction, the repeated references to section 12, this is a Poorly Disguised Pilot that the producers were using to test the waters for an x-files like section 12 spinoff.
Overall, I did not enjoy it. I don't seek out this kind of film normally, and I might have enjoyed it if it had led to anything interesting happening, but ultimately it has not left them with any further progress. All the dramatic moments between the away team and the "others" they hallucinated were basically "then they woke up and it was all a dream", so no relationship progress there. And within themselves, aside from more unresolved trauma, Spock seems no closer to aligning his human and vulcan selves, La'an hasn't really learned anything new about her violent tendencies she didn't already know from the last episode, and Kirk never even got to have the chat with his family because the network apparently cut out.