Things that with the passage of time and changing circumstances, were the movie being made today simply don’t function as they once did plot-wise. For example:
All About Eve: Eve ingratiates herself to Margo and the rest by seeing every performance of Margo’s play. Not only in this era of stalkerazzi is it extremely unlikely that she’d be invited backstage, with Broadway ticket prices being so outlandishly expensive there’s no way she could afford it.
Rounders: The recent crackdowns on underground poker clubs in NYC make a good chunk of the setup less likely. Also, because of the extensive availability of online satellites it’s doubtful that Mike would feel the need to risk his bankroll at KGB’s in the opening scene. Even if he did and he still wanted to play the World Series of Poker, he’d just get himself a cheap PC.
Sorry, Wrong Number: Caller ID, *69 etc. would make it ridiculously easy to trace the calls back to their source. The cops might still not believe her but she wouldn’t have to spend all that time trying to figure that part out.
I’m less interested (despite my own last example) in stuff that’s purely technology-driven, like something taking old computers a long time to do where modern computers could do it much faster and so on. Other examples?