The surface problem isn't that naive evolutionists think humans descended from (time-traveling?) extant monkeys. The surface problem is that they don't understand the difference between apes and monkeys, even though this is very easy to understand; and they don't understand that there has never been a common ancestor of all and only the monkeys, or that the common ancestor of monkeys and apes was neither a monkey nor an ape.

But these are all, as you rightly note, nitpicky taxonomic details. Given the folk-blurriness between 'ape' and 'monkey,' and closely related groups, it's not a particularly serious error to misidentify the common ancestor of humans and monkeys as a monkey (or as an ape). The deep problem here is not an error of fact, but an error of strategy; the ignorance of the evolutionist is not only weakening his/her case should the creationist spend 5 minutes on Google, but also is causing him/her to sacrifice a prime teaching moment. This common misconception about monkeys/apes is a fantastic opportunity to correct a misconception (thus undermining the creationist's easy confidence in the most frequent soundbites) and springboard into an explanation of what evolution actually is, of the mechanisms and scope of common descent.

There's also the very closely related error of presuming that evolution is 'directional,' thus that humans are 'more advanced' than their cousins, who have 'evolved less' and thus surely resemble the common ancestor more. In most respects and in most cases, this is misleading.