While you certainly can't blame the maternity ward for that wacky series of events--the parents were assholes and the kids were identical twins--what about babies that don't look like each other? That's a pretty common switcheroo in the entertainment world as well. It's happened multiple times on the soaps All My Children and One Life to Live, as well as The Ghost Whisperer. It's so common, TV Tropes has a whole section devoted to it.
Shit Gets Real:
It turns out there's a creepy amount of truth to this one: Apparently maternity wards in real life aren't too discerning when it comes to what parent gets what child, just so long as the little crumbsnatchers are out of their sight eventually.
For example, Marti Miller and Sue McDonald had no idea their families had been switched until one mother fessed up... 43 years later. Or Kay Qualls and DeeAnn Angell, who were switched in 1953. One of their mothers even told the maternity ward that they had fucked up. Unfortunately, she was ignored--a fact that can be attributed to the 1950s being a much simpler time, when having a vagina meant you didn't get to be taken seriously.
As for twins being separated, it happens so often that a research center was opened to study how their lives are different. Hell, even the classic "twins being mistaken for each other" gag has actually happened: In Spain, a woman discovered she had been separated from her twin in a Canary Islands maternity ward 28 years earlier, when she randomly stumbled into a shop that her sister frequented. And, since we stopped reading immediately after we verified our claims, we can only assume one turned out to be rather fussy and useless in a fight while the other spent her entire life relentlessly training in the art of kickboxing, and upon meeting decided to team up and avenge their master's death while learning valuable lessons about life from one other and doing the splits. Either that, or they just made out. That's pretty much all pop culture has taught us that twins do.
Van Damme is prepared to do both. At the same time.