Technically any woman married to Dent would, in the Joker's eyes, be guilty of bigamy because Dent is two people, even if those two people reside in one body (hence "the Harveys").
It's possible, but if that's the case, wouldn't Gilda be the one who was guilty of a crime (bigamy), not Dent?
I really got the feeling Joker was pointing out Dent's indiscretions. "There's a lot of things people in our positions can get away with...murder being one...WIVES ain't two of them."
Dent's the murderer (not Gilda, except via TLH, but Joker doesn't know about that and I don't think that's what's being referenced.). Also, "wives" is in plural.
Joker's next line: "Bigamy is like tax evasion. Once a prosecutor has a crime he can try in the public eye..."
A reference to Al Capone (busted not for being a gangster, but for tax evasion) - Joker's suggesting that the justice system can't target Dent for being the mob boss of Gotham, but they could get him for HIS bigamy.
Incidentally, Dent later says "Loves a funny thing. Funnier than YOU'LL [Joker will] ever be. I knew there was a chance this could happen...That his [Dent's] happiness could be compromised...So I made certain it COULDN'T. I have a man on speed dial will make EVERYTHING in that case there disappear."
(Sorry for the bracketing confusion...those lines start off being told by Dent, then by Two-Face, then Dent again at the end).
I think the implication is that Dent's happiness is somehow related to the marriage issues - and that whatever is in the case is related (if not, it's still probably something damning that can bring Dent down) and can be used against him. But what could be "impossible to steal" in that case that's related to Dent's supposed marriage issues? Certainly not marriage licenses or court documents - why would they be "impossible to steal?" And how can a man on speed dial make them disappear?
I don't understand the marriage issues are being discussed. Nor do I understand what's in the case (though clearly Dent's very concerned about it). Or how it could be made to instantly disappear with a phone call.