My wife and I are new to Ballroom dance, and after reviewing and practicing the basics we've learned from various videos and on the Internet, decided to take formal, private lessons. We've been attending an Arthur Murray studio in the Green Bay, Wisconsin area.

However, we've seen a lot of negative slams against the AM method, primarily on the rec.arts.dance Newsgroup. Nothing solid has been said, though; it seems more of an 'attitude' thing. Is there something we should be aware of by trusting the Arthur Murray method? We aren't really certain about expecting to eventually compete, but we are very serious about learning proper technique, theory, and steps.

Any thoughts or comments on the Arthur Murray dance studios would be appreciated.

I'll wade in with some comments about Arthur Murray Studios. I've been taking lessons for about three years, all at various AM studios. My experience has been very positive, but I've also been very lucky with regard to the specific studios I've been at, and also with regard to my instructors. The instruction at any studio, AM or independent, is only as good as the teachers who are there. Even with the AM "method," and a common syllabus, not every AM studio is a cookie-cutter version of another.
A key thing is to COMMUNICATE with the instructor, and the franchisee. If you want to focus on technique, ask them about the best way to focus on that - preparing for competitions is a good incentive for both you and your instructor to focus on those details. If your instructor knows that you really want the details of technique, they may plan your lessons slightly differently than they would if they thought you wanted only a "social" dance education.
I, too, wanted to focus on style and technique in dancing. I've never really been all that caught up in "method" of teaching - dancing incorporates a entire range of elements from poise and posture, to footwork, to lead/follow, etc. Just because one "method" focuses on, say, footwork first, whereas someone else's "method" focuses on, say, posture first, doesn't mean that one method is right or wrong, or better or worse - in the end every "method" aims at working on all the elements. A lot depends on how long the student can stick around to learn each element and how to put them together. Each element may need to be learned in various "layers" - so that, for instance, you are not going to learn all the hundreds (or so it seems!) of intricacies of Cuban Motion in one lesson - you will probably start with a very basic component of Cuban Motion, and as you become more comfortable with it, the AM "method" will refine it, add another component to it, etc. Some people who slam the AM method may have stopped taking lessons before they learned all the components of each element, and feel as though they didn't learn anything when they find out that other people focus on different aspects of an element. I'm at the point where I can take a few coaching lessons from independent coaches, and they have told me that I've been taught some pretty solid skills.
AM does try to "sell lessons" and they are criticized for seeming to push people into long-term contracts - keep your eyes open, and know where you want to set your limits. But also be aware that if a studio knows that they have, say, 15 lessons to teach you something, they can better plan your lessons, than if they don't know from one week to the next whether you'll be back or not and then try to cram too much into a lesson.
AM wants to sell lessons, but if they turned out consistently awful dancers, no one would take lessons from them. My instructors have been just as committed to teaching people to dance well, and I have seen some pretty darn good dancers who learned through the AM "method." Be realistic and be tolerant with regard to reaching your goals, and have some fun along the way!
I've probably gone on too long, so feel free to e-mail me privately, if you want to delve into any specifics. Meanwhile, I'll get back to preparing for my next competition. . . .

After attending a number of comps and watching the dancers from different studios, I'd steer clear of AM except for casual social dancing.

Hmm - I'd still say it depends very much on the studio you are affiliated with - as for AM studios, I wouldn't tell, for example, Bob Powers/Julia Gorchkova, or Jesse Smith, or Pat Traymore, or Christian Perry (the swing "guy from the Gap commercial") that they should stick to teaching casual social dance!
I'm pretty cautious about judging a studio on the basis of comp results alone. Some studios (both AM and independent) take only their "A Team" to big comps - but I guarantee you that, back at "home" there many casual dancers who have been left behind even though they are the bread and butter of the studio. However, I've also been at other AM studios where they encourage EVERYONE to go out and try a comp, just to see what happens and whether they want to do comp dancing. And in those cases, AM, unlike a lot of independent studios, will not insist that you have costumes, or totally prepared material, etc. to go out and see what competition is like. But it also means that you don't always see the best dancers from the studio.
Once at the comp, different studios/instructors have different goals. My instructor, for example, will never have enough entries to be in contention for the Top Instructor money - so he's got nothing to lose by unexpectedly trying some new stuff out on the floor. Additionally, his "Comp Team" consists of a bunch of Type A overachievers who WANT to stretch themselves as much as possible, who WANT some new stuff to try "on the fly" - so they enter comps at their current level and one "above." This tactic does NOT always result in stunning victories! Oh well. Many times, other instructors enter their students at their current level and one that is seemingly "below" (categories seem to be based on level of patterns, rather than your level of technique, so it is easy to "fudge" these things: dancers with bronze patterns-gold technique can be in the same heat with a dancer who is still bronze patterns-bronze technique. Fair? - well, just accept that it happens; but which dancer is being "pushed" more?). This tactic results in lots of top finishes for a studio, keeps students happy, impresses on-lookers, and keeps the teacher in contention for the Top Instructor Award. If the difference between these approaches matters to you, then be honest about it and talk to your instructor. Sure, it's wonderful to win, but for some dancers, improvement is what they judge themselves by.
Again, I'd say the key thing is to COMMUNICATE with your instructor/studio about what your goals are, and about their approach to dancing socially and/or competitively. And then, give it plenty of time!