At the end of the episode, the Doctor asked Kim from the other ship if his counterpart had a name. Kim said he didn't really have time to ask. Really? He'd been serving with him since the beginning of the voyage. He didn't have time to ask? Also, is it me or did the two Janeways seems to be a little too close to each other's personal space when talking? It's probably so they could both be on the older-sized screens, but still...they were almost close enough to smooch!
Perhaps an error in the script? He should 've asked Kes that question, who was over on the other ship for a short time and it would also have served continuity better (as Kes was the one encouraging him to search out a name in the first place). Well, Janeway is supposed to be something of a 24th century version of Kirk, and we know about him that kissing himself must have been his lifelong ambition
Honestly, I didn’t even understand that question in the first place. The split explicitly took place within the episode, in the middle of delivering the baby and the ongoing crisis, why WOULD the other Doctor have taken the time to effectively pull a name out of a hat?
Regarding your second point-the Janeway's being so close I think was almost intended for titillating the audience. Though I'm not sure but I suspect it. Isn't the doctor talking about his counterpart? I mean they were the same ship split into two for like ten-fifteen minutes. So the doctor would have been the same prior to this.
Data and Lore (and Dr. Soong) were shown in a similar fashion in TNG. But you also have to think of what was going on in the scene, since if it was a private conversation, then they’re going to be close.
Maybe but the whole "their lips are centimeters away they might start making out" appeal may have been there? I admit I could be misinterpreting it but I think the idea of titallating the audience could have been at least a partial motivation for showing them so close together? Though I admit I could be wrong.
At a convention Kate Mulgrew mentioned that she wasn't allowed to move in any direction more than eight centimetres away from the position in which she had to stand while the scene was being filmed. I guess it had something to do with film-making technology back then.
Correct. She stated it was pretty unforgiving at that time. Not only are 'they' close but you can imagine the line dividing the shot. It transparently shows how limited the affect was in '96.
It's an example of the selfishness of the EMH, amidst the tragedy (losing their Kim and Naomi) and damage that the crew were still recovering from all he could think of was himself.