My personal choice might seem a bit odd, but I'm going to go with The Insider, Michael Mann's movie about the big tobacco whistleblower.
For the most part, the movie is a very credible, down-to-earth drama. But midway through there's a bit where the wife goes downstairs where the computer is, and without warning (or user input) an email delivers and opens itself, playing a big red animation that goes WOMP WOMP WOMP WE'RE GONNA KILL YOU WOMP WOMP WOMP.
I expect stupid shit from movies like Hackers or The Net. Ridiculous computer-magic just comes with the territory. But when it comes out of left field in a movie with plenty of verisimilitude otherwise, it's especially annoying.