First off there was a lot of talk about the relationship between Faraday and the woman in the hospital bed. We also had some thoughts about who 'Ellie' the British woman who walked Dan out to the h-bomb was, and her relation to everyone was. I'm gonna break it into two parts.
Teresa Spencer

This was the woman who we first saw in the photo from Dan's old lab. This is the same woman who is in the hospital bed when Des goes to find her. We had some theories that she might be Dan's half sister. I really think that this is wrong. I think the main reason we came to that conclusion is because of the conversation that Faraday has with Ellie on the Island. In the conversation that Des has with Teresa's sister she speaks of Dan not like a brother at all and she mentioned that their father had died five years ago. I suppose it is still possible that their moms are the same person but the more I think about it, it just seems to circumstantial. As for Ellie.
Ellie

I am even more convinced that this is Dan's mom. The conversation that they have as they walk out to the bomb is about why Dan is looking at her funny and he says that she reminds him so someone "He used to know." This was the comment that made a bunch a people think, OH! she looks like the Teresa! She is gonna be her mom!
I think this is the wrong conclusion. I think he is using this line as a cover for "You look like my Mom, because you are." The "real Romeo" line that Ellie uses is more of a like, Ha! His mom thinks he is romantically interested in her.
As for Ellie being Ms. Hawking well. I'm totally convinced of that. Ms. Hawking knows about time travel, a lot. I think we can thank Dan for telling her that it exists in this episode. She is in LA, we know that because at the end of episode two she is talking to Ben who is also in LA. Dan's mom is also in LA (coincidence?). Finally when looking for this picture of Ms. Hawking I searched 'Hawking' on Lostpedia and it came up with the name 'Eloise Hawking'. Sorry if that is considered 'SPOILER' but it got me too. Okay well I hope some of this makes sense in some way and I look forward to seeing what you guys think.
-Travis