I did an away rotation at the beginning of 4th year b/c I wanted to attend a program that none of my advisors had ever heard of. I thought this program was IDEAL based on its descriptions, but everyone kept telling me to avoid a program without an attached medical school - as a compromise, I decided to do an away externship there to see if what the program was like. And, in all honesty, I am very glad I did - as Felicity said, it really did open my eyes to different ways of practicing. For example, this "warm and fuzzy" program had lovely faculty and no call, but the in-patient atmosphere was not as collegial and learning-centered as I'd become used to in medical school (questions are not encouraged unless given permission to speak; residents preferred the externs to be seen but not heard; a bit more hierarchy than I expected). But, I got a chance to work with schizophrenics and spend a lot of time with them every day - something I hadn't managed to do at my home institution - and I LOVED it. Completely loved finding out that one really can talk with people experiencing vivid psychosis, and sort of understand their inner world... Connect with them and even develop therapeutic relationships! Blew me away (had previously thought you could only give them meds and wait).
So, I valued the experience on many levels - learning about the program's "atmosphere" and how well I meshed with the residents, learning how to connect with patients in active psychosis, and how gorgeous california weather is... *laugh*
On the down side, this was a huge upheaval for my family (travelling across the country for a month), expensive (airfare, car rental, and rent), and a little stressful (learning a new computer/hospital system, navigating a new city, etc).
As an aside, please take care in posting anything negative about your extern experience on these forums, because I received extremely irate e-mails from a resident who recognized herself in one of my posts (despite no name or institutional id's included).
I've heard from many folks in these forums, who did away rotations at institutions they really wanted to attend, and then they realized they didn't like the program as much as they'd thought. On the other hand, I've also heard from people (in psych) who did an away rotation at competitive schools (UCSF, Cambridge), and did NOT receive an interview invite - so it doesn't guarantee an interview at those 2 schools anyway.
I'm not sure it's the best thing to do to improve your chances, but I agree with felicty and beatrice, that it's a fantastic way for YOU to check out programs you think you'd really like to attend.