1. When Jimmy was acting out at Bert's restaurant, I thought Penhale was great when he gently said "There's something wrong with you Jimmy." Sometimes he seems to be Portwenn's version of the wise fool.
2. I have never been able to figure out what Pauline says in the scene in the question where she is interrogating DM about Louisa's appearance in the village. He says that she never intended to stay with him, etc., and Pauline has her back toward him at the sink and mutters something, to which he barks: "I am not." Does she say "heartless"? "unkind"? ????
3. Not quite sure how I feel about the subplot of "bi" Jimmy. (And by the way, why doesn't DM have a computer in his office and always have to use Pauline's?) It really wasn't played entirely or even mostly for laughs, and it did show DM being uncomfortable with these matters but attempting also to be compassionate. Interesting.
4. The scene at the beach where there is a very large shot of DM stepping on the hand of the child. We're definitely meant to notice this, and it seems to be in aid of setting up a situation which riles up the headmaster so that he pushes Louisa. But, is also shows why Louisa might be uncomfortable with the idea of DM as a father -- when his initial reaction to a child's pain -- that he caused -- is to tell him to stop whingeing. I found that deeply uncomfortable. And a clear indication of how his parents treated him.
5. Louisa says at the end, "Thanks anyway, Martin" to which he clearly takes offense. And he did try heroically to help in the situation. But clumsily, and convinced he was right and seemingly making the situation worse before he saved the day. I agree with Mona that on balance, the "anyway" was gratuitous and unnecessary.
6. We had a conversation a few pages ago about why Louisa didn't go through with the marriage, and one thought was that she knew she wanted children and decided that was not a realistic expectation of a marriage to DM. Holding on to that thought helps explain, I think, why she didn't tell him when she knew she was pregnant. I don't think she planned to return to Portwenn, but the implication is that the school let her go (or made things very difficult for her). But the fact that he wasn't told clearly upset Martin and made it easier for him to rationalize/believe that she didnt want him involved.
7. Whatever she wanted or hoped for in stopping to see DM, she was thrown for a loop when she saw Edith and leaped to the conclusion that he was in a relationship with her. Both were too agitated to sort that out on the spot, but of course she could have later pressed him further. But I think her pride would not let her do that, and she might have felt that given that she had rejected him, who was she to question his new relationship.
A few comments on your comments, NewPark:
1. DM does have a laptop at some point in the series, later on, I think, S5, which he uses in his consulting room. Yes, when AR comes in once, he is using it. Also, as a physician doing research on the internet, I usually start with either Google Scholar or with Pubmed or Medscape, etc. I do not go to well, the site DM wound up on....And, how our medical journal reading and medical journal author DM wound up there we will probably never know!
2. "Thanks, anyway, Martin" is definitely unnecessary, and even a bit mean, NewPark, and really does not show LG well, in my opinion. I support DM getting offended by it. It's an early signal of LG we see play out a lot in S5--her inability to recognize his help (even risking his life in the sea to do so!) and say anything gracious about it.
3. "But the fact that he wasn't told clearly upset Martin and made it easier for him to rationalize/believe that she didn't want him involved." I see no other way for DM or any other man on the planet to interpret LG's actions, than she didn't want him involved. That's not misreading by DM; that's reading what LG was saying and doing accurately.
4. LG making assumptions about Edith, and her relationship with DM, is another repetitive bad habit of LG's. Need we say "Godfather apology"? A mature, well-adjusted individual could easily ask about Edith without assuming DM has replaced her and doesn't want anything to do with her. Even if she doesn't ask DM, Pauline would certainly give any gossip along those lines. Unfortunately, we see LG falling into bad habits from their first meeting, and initiating the resultant havoc. Not solely being the cause, of course, as DM plays his clear part once things are spoiled in the first episode, but LG was, I feel, the one who started them off so very badly.