Hopefully my current moderation stats speak for themselves, but here's my answers! Wish I'd spent longer on the nomination thing, meant to edit it before the initial period closed :)

How would you deal with a user who produced a steady stream of valuable answers, but tends to generate a large number of arguments/flags from comments?
I'd leave some extra comments where appropriate suggesting how to better go about things in the future, perhaps highlighting the use of chat over comments when discussion is required. If the activity doesn't change then it'd be time to send a moderator message to the user, encouraging them to maintain their enthusiasm and engagement but to try and make changes to their approach.
How would you handle a situation where another mod closed/deleted/etc a question that you feel shouldn't have been?
First check to see if the question has been modified since, this has happened a few times and often the edits make the question suitable for reopening. If that's the case then I'd reopen it, otherwise I'd probably have a quick chat with the other mod to discuss the question.
What can you do as a moderator to be welcoming to new site members if their questions or answers are flagged?
Same as I do now, leave a comment welcoming them to the site and suggesting how to best proceed, i.e. do research, post code etc. depending on the scenario. Out of the box comments aren't all that friendly towards new users.
What unique value will you add to SFSE as a moderator compared to your current member role?
I'm a moderator right now! My ultimate goal is for SFSE to be the best resource it can be. It still feels like my baby even though it's all grown up and I think my moderation activity shows that I care about the site a lot.
Moderating SFSE does take a good chunk of my time, but if I didn't enjoy it or care then I wouldn't be doing it!
Other than yourself, and existing moderators, who of the other nominees is most worthy of a moderator position?
I think Samuel is the clear choice here, though I'd like to see some more personalised comments to new users etc. when dealing with reviews as opposed to out-of-the-box comments. His enthusiasm is clear to see to everyone though!
Is it possible to prevent degradation of quality in questions and answers as the membership grows, and if so, how?
It's definitely possible, through more moderation from the community at large. There's been a huge influx in the number of new users quite recently, and often it appears that they have not read the help and FAQ. Commenting with friendly suggestions is a good start, but we need more people to spend time reviewing and flagging. Also users need to be encouraged to actually take their time when reviewing, there's been a few cases where things have been reviewed and left as-is when something is clearly wrong, and the posts have been subsequently flagged.
It also takes effort from the moderators and power-users to spend time cleaning up questions that they see.
What do you see that you can do as a Moderator to encourage new users to both vote up the helpful answers they receive and accept answers when questions have been solved; in essence educating them on how SFSE is intended to work?
Generally when I see these scenarios I add a comment (being sure to mention them where required) explaining why voting/accepting is important so that they have the opportunity to take action.
What do you plan to do to see that questions are appropriately preserved for posterity; ensuring they'll show up in a useable manner when searched in the future?
I check that questions are tagged properly, and do make edits where new releases have changed the status quo, but also I tend to edit questions that use abbreviations. For instance, many questions include "VF" instead of "Visualforce" in the title/body, and that's not going to help people searching the net. Although we all know what "VF" means in the context of the site, I don't think many people are likely to use it when looking for information in a search engine, they're far more likely to type "Visualforce" in full.
How much time do you believe you have available each week (on average) to devote to moderation and how do you see yourself allocating that time among the responsibilities you'll have?
Right now I probably spend anywhere between 4-10 hours per week on the site, and with every visit comes moderation. More than a few times I've come here to look for an answer to a problem, gotten distrated by moderator flags and then closed the site 30 minutes later having totally forgotten what I was doing in the first place.
How, if at all, do you see the 3 moderators dividing up some of the responsibilities of managing this Q&A site between the three of you?
To date there's been no need to divide the work up as such, with three of us being in substantially different time zones it's been a rather natural process. Personally I believe that unless the workload becomes overwhelming (which it shouldn't on a community moderated site) that there should be no artificial division of labor. Moderation should be dealt with in a timely manner, which is why if I see a flag when I visit the site, I deal with that before anything else.
I want to keep doing this because I love this site. Thanks for reading :)