So, when reading this, keep in mind it is coming from another 3rd year, and I probably know just as little about this whole process as you.
Having said that, I am sure your advisor is great, but according to the people i know who are already in ortho, it is a different world than other specialties, and most people outside this world don't necessaily know it well. Every Ortho attending and resident I have spoken to has said it is expected that, as an ortho applicant, you will probably do at least one away SubI (and often 2, since the field is so competitive)... people who don't do aways are in the minority. An away is considered one of the top factors in choosing residents
(read Bernstein AD, Jazrawi LM, Elbeshbeshy B, Della Valle CJ, Zuckerman JD. Orthopaedic resident-selection criteria.
J Bone Joint Surg Am. 2002 Nov;84-A(11):2090-6.). This seems to be particularly important in the following situations:
1) The site is one of your target programs.
Some attendings have explained that a good fit can give a mediocre paper applicant a much better shot of matching to a program... its hard to rank an unknown student over one you know well and respect. The calculated risk here is that, if you fit in well, it can really help you. If you don't fit in well or you really suck it up, it can be a death sentence (but then again, if you don't fit, its probably best if you don't end up there anyway)
2) The site will help you get a "big" letter.
"Big" can mean moe than one thing... A) a well-known surgeon,

someone impartial (v. home program faculty) with a strong opinion of you, or C) "someone who knows someone" at other programs where you are applying.
3) The site is in a region other than your home school where you plan to apply.
Everyone I have spoken to, in multiple programs, has made this point... first, it proves you are willing to move to this new area, and second, it gives schools in that region an opinion from a program they can better relate to
4) Regarding rotations in other specialties- not to be negative, but I don't think any ortho attending I've spoken to would care one bit what the guy in anesthesia has to say, and doing an away in another specialty doesn't get you any contact with residents (whose opinion can play a big role in defining rank lists)...
Of course, if you want to do another away in adition to your ortho, it can give you a better feel of the hospital, but its not going to have much effect on your chances of matching there
As far as the city/ hospital/computer system/faculty knowledge mismatch, consider the following (and this is just my opinion)...
1) You have probably been learning new systems during every 3rd year rotation, and I am sure you did fine... there isn't any reason this should be different.
2) People will know you are new to the system and will probably take that into consideration as long as you try hard and figure things out at a reasonable pace.
3) Few programs would want to match their entire residency class (or even most of it) from their own med school... they want the best students. In fact, home students as a group are probably at an overall disadvantage, because only so many spots will go to home students.
So, that's pretty much the entirety of what I have learned by talking to a bunch of residents and attendings... take from it what you will. Good luck! Hope to see you around on interviews!