Perhaps some of you have checked out Ringer, the new Sarah Michelle Gellar series featuring a young woman on the run from the mob and the law who is given reason to believe her twin sister is dead. Seeing a chance for a fresh start, she assumes her sister's identity and - at least in the pilot - does a good enough job of replacing her that no one suspects a switch has happened.
The premise is similar to ABC Family's The Lying Game, where two long-lost twin sisters meet after being adopted by different families. The sister raised in privilege has the sister raised in foster homes switch places with her while she continues investigating their past. And again, no one seems to catch on immediately that Foster Sister isn't Privileged Sister.
I've known a set of twins or two and I'd have to say that it's really unlikely that even sisters who grew up together would be able to maintain that sort of ruse for long. Even when they look exactly alike, there are too many subtle differences in manerisms, behavior, and even vocal inflection. So how does the script get around this?
In both cases, the other people in the replaced person's life is unaware that a twin even exists. As silly as it seems, that's enough to clear the basic suspension of disbelief. If my wife suddenly started acting differently, I know my first thought would likely be along the lines of "Is something bothering her? Did I do something to tick her off? Is she under a lot of stress?"
As opposed to, "Holy shit! My wife has clearly been replaced by a twin that I don't even have any way of knowing existed." Some might call it a contrivance, but I think it works because from the POV of everyone in the twins' lives, they have no reason to suspect a switch has taken place.
I also call this the "Marty McFly Rule." A while back, I did a series on Back to the Future and a few people wrote in saying they never bought that Marty's parents didn't recognize their own son as the guy who helped them get together 30 years earlier. I've never questioned this, for the following reasons.
First, it's been 30 years between them meeting "Calvin Klein" and they only knew him a week. My high school days are less than half that distance in the past and I know I'd be hard-pressed to come up with a crystal-clear recollection of someone I only knew briefly then.
Plus, if I encountered that same person 15 or 30 years later - or rather, someone who looked exactly like that person - my first thought wouldn't be "They must be a time traveler!" It would be, "Wow, that guy looks a lot like someone I used to know." You also have to figure that with their son, they've seen him grow up into that face, so it's not as sudden as seeing this guy materialize out of the blue.
So that's what you have to keep in mind with suspension of disbelief. Some times it's about selling an idea to the audience, and other times it's merely about accounting for the characters' own disbelief.