I've been hoping someone would bring this up, being interested in points of view on this topic since I'm getting past the halfway point in my own program. I think it depends on a number of factors.
The synopsis is: it helps, but not always. The top three specialties for MD/PhDs has traditionally been IM, peds, and pathology. These are not particularly competitive residency spots to begin with. Also, because these specialties have traditionally been the ones with the MD/PhDs in them, they are the ones who will put the MD/PhDs in a separate pile and give them alot of preference. Neurology and Psychiatry are two other increasingly common MD/PhD specialties. They are also not particularly competitive.
I'm not saying the MD/PhD is meaningless. It does add alot of weight to your application. However, if you're going into a very competitive specialty that's not traditionally filled with researchers or just so competitive that everyone has alot of reasearch, it gets alot trickier to assume the MD/PhD will get you where you want to be. In a specialty like say, Radiology, where there's mostly clinical emphasis placed by programs, the MD/PhD will help, but it doesn't seem like a ticket into top programs. This is how someone from my MD/PhD program matched far down their list to a lower-tier academic Rads spot last year even after doing their PhD in Radiology. Meanwhile, someone else matched to UCSF Rads and didn't even do their PhD in Radiology. That's because some of these people you see getting very competitive spots in very competitive specialties have the board scores and AOA statuses to back them up. They would have been competitive applicants had they not had a MD/PhD. When I was investigating neurosurgery as a potential residency, I noticed that the two guys who matched neurosurg from my program that year were both AOA.
The other issue is regional selectivity. You're going to be shut out by community programs and other less research-oriented places. If you have a strong desire to be somewhere, this is really going to narrow down your choices for residency. That being said, do we as MD/PhDs really want to be at community programs anyways? Unfortunately however, the top research programs are the most competitive ones (just like med school!), so everyone speculates about the possible applicant who is very strong in research but can't match because they don't have the board scores and clinical grades for the research programs and can't get into a community program. I've never seen this happen. I've seen a number of MD/PhDs elect not to do residency or leave their residency, but I haven't yet seen one try to match and not.
I hope that sums it up alright. The MD/PhD stands out on an app, but you have to take MD/PhD matchlists in with an informed eye.