Two kinds of assertions that seem particularly likely to be underdetermined -- or, more generally, asserted with more confidence than is justified -- come to mind.
One is a judgment based entirely on a single news report. Even if all the facts in the report are accurate (hey, it could happen), it's unlikely there will be enough facts to settle any disputed points raised in the report.
The other is a divination of the motive behind someone's action. Although pointing out the personal failing that caused someone to do something bad (or, for that matter, the personal virtue causing something good) can be nearly irresistible, it should nearly always be resisted. Often enough, it doesn't matter, and possibly even more often, you simply don't know.