The problem is almost certainly not with the Straight Dope itself, though it’s quite possible that there’s a misbehaving ad being served up. Technically that’s not an ‘SDMB issue’ since they have limited control over what ads are being served (though if this is in fact an ongoing issue, perhaps a change of ad vendors might be in order).
It’s also possible that the problem is on your end. Malware in the form of a browser extension/add-on/plugin wouldn’t care what site you were on. Neither would a rogue program that got ‘stealth-installed’ because you forgot to uncheck a box the last time you downloaded something.
What browser are you using, what version, and what, if any, plugins and addons do you use? Is Java enabled, and up-to-date if it is? What about Flash? Adobe recently (Feb 4) released a fix for a zero-day exploit; did you install it?
For the record, I run Chrome, with Adblock, and I have never had any sort of ‘malware experience’ browsing the Straight Dope. I realize I run the risk here of being ‘one of those people’, but the fact is that malware problems are more often than not ‘self-inflicted’.