I just listened to the PM O3 cast today and I'm wondering if I should do O3s with the members of a Scrum software development team or if it would be overkill.
Our overall project is about 6 months long, and we work in 2 week iterations (like mini projects). We have a 15 minute meeting every day to give status updates and plan our work for the next day. Each task is ideally only a couple of days long, and team members generally collaborate on these tasks.
My team consists of 9 people, including programmers, testers, technical writers, and trainers. Six of us are dedicated to this team, and the other 3 are on other teams as well. Several team members are remote, and we all work from home the majority of the time. We get together for a few days every 6-8 weeks. The team composition will remain fairly consistent over the course of the project.
As the Scrummaster, I am not even really a team lead. I don't direct the work; we're supposed to be a "self organizing team." My function is to manage the paperwork, run the meetings, coach the team on following the Scrum process, and help remove problems that team members encounter (as well as be an individual contributor).
Our manager has about 25 direct reports - mostly remote - and does not do O3s.
Would O3s help surface problems and build relationships (especially with remote team members) or are they excessive given the short iteration length and daily status/planning meetings? How should I modify the PM O3 for Scrum?

Yes.
I don't remember the specifics of that cast, so I can't think of specifically how to tailor their suggestions for scrum. However, if you have a project that goes 6 months - even if you are doing 2 week sprints, you are still going to have the team for 6 months. I know you say that you are supposed to be a "self organizing team" - however, I bet if deadlines are met, some of what you do will be scrutinized. Relationships will only make your work better.
John
typo
sorry, last 2 lines should read:
however, I bet if deadlines areN'T met, some of what you do will be scrutinized. Relationships will only make your work better.
Scrummasters need friends too
Certainly use O3s.
As Scrumaster one of your key responsibilities is identifying problems (real or imagined). The more you know the team, the more they are likely to open up early in the process of going wrong, rather than when it has gone wrong.
Think of it as Scrummaster spidey-sense.
Scrum & O3s
I think it depends on how your organization has implemented scrum.
We also use scrum and I wouldn't consider recommending that our SM's use O3s. Unlike regular "projects" in the classic waterfall sense, there's little or no project reporting relationship with the individuals on a scrum team and their scrum master.
The other posters do have a great point about creating relationships with the individuals and working closely with them to surface problems, I just don't think that running an O3 in addition to the daily scrum is going to get you the benefits that the PM O3 provides to a PM who is working waterfall.
That said, the other posters do have a point about the importance of fostering relationships with the rest of the team, and perhaps you might accomplish what you need with a weekly coffee?
Alternatively, if your organization is just cargo culting, then yes - jump on the PM O3s. its quite possibly that you'll get more benefit from the O3 than the daily scrum if your organization isn't practicing real agile (which I've been known to call [fr]agile :).
Don't do PM O3s. You're not
Don't do PM O3s. You're not a PM. Do coaching O3s if appropriate, or leave the team alone.
The whole point of daily stand-up (and demos, retrospectives, and sprint planning) is to make doing a PM O3 unnecessary. You've hit it on the head: you're not a PM. Don't try to be one. Get out of the way, and let the team succeed. It's not about you; it's about them.
If you've set up the scrum board, burn down, and other "informational workspace" artifacts correctly, you ought to be able to get all of the information you'd get out of a PM O3 from looking at the wall, without interrupting the team. Keeping folks from interrupting the team is half your job. If things aren't set up so that interested parties can get the size in inches without interrupting anyone, look for the source of that problem in concentric circles around your desk.
Unpacking the SM role a little, a SM is supposed to be one part coach, one part impediment remover, and generally winds up with the tracker role as well. (I'll skip the rant about how the role creates a silo that keeps the team from getting to being really self-organizing.) If the manager isn't doing O3s with the team -- and with a span of control of 25, it would be hard to -- who's looking after the team's professional development? Even if you're not the one doing their reviews, it is explicitly in your purview to take responsibility for your team's maturity and skill. Regular coaching conversations with team members are entirely appropriate toward that end. (But please don't inflict help where it isn't wanted.) Have you spoken with the manager about the team's development? Do you have an O3 with the manager?
One last point: please don't use waterfall-style PM O3s as a Band-Aid if your team is doing Scrumbut. If your organization is a "cargo cult," that's an impediment to your team that it's your job to remove.