That being said, I'm not at all surprised that it happens and frankly not very worried: it's on a ridiculously small scale. There's a reason the NYT article focused on specific stories—the overall stats aren't exactly that scary.
Of 639 seizures in 2012, 128 were legitimate. While 80% false positives doesn't seem good at first glance, consider that it's out of over 700,000 reports. Less than 0.1% of reports actually led to people's money being wrongfully seized—that's a low enough rate that it's hardly worth worrying about. If anything, I'm more worried that they're not catching more money launderers and tax evaders (only 128 seems awfully low in a country of 316 million).
I think most of us would be hard-pressed to come up with a system which had a similarly low error rate. Paypal, for example, hardly does any better. Probably the biggest problem here is just that we don't provide effective enough mechanisms for remedying it.
But this article doesn't even provide sufficient evidence of that. Take the Hirsch brothers who have been having trouble reclaiming their money. While that's unfortunate, I can totally understand how an all-cash family business which paid vendors in cash might have trouble providing adequate records. If I were with the IRS, I would have flagged them as well—tax evasion runs rampart in those sorts of family businesses.
Yes, there's a small problem in our justice system (that it's hard to correct false positives). But it's hardly something the average person will ever be affected by. Focus on the scarier things, like systemic wiretapping.