The default/"best" answer is "a Terran and a Klingon", both in the singular.
Various other singular versions are also accepted.
(No mixed versions currently, though I suppose they should be as well. I'll see whether I can add some.)
Note that tera'ngan is a "Terran" -- "human" not the best translation (and has its own Klingon word, Human). Not all human beings necessarily come from Earth, at least not in an era of spaceflight and planetary colonisation.
Since Klingon grammar so often requires a different order of words from English. We point out those areas where the grammar allows the word order to match by requiring you to maintain the word order in your translation if the grammar does not require you to change it.
Klingon grammar requires you to place the noun conjunction at the end, so the je cannot match the and in placement. The names, however, can go in either order in either language and so the order should be maintained.
While the meaning does not change much, there may be reasons why one name is being said before the other. Think of two authors fighting over who gets listed first on the book. Sometimes the order is important even if it doesn't change the meaning.
So the bug in the software was not in marking it as a typo, but in accepting it at all. In the Klingon course, such unnecessary reversal is typically marked wrong.
Ah. I see. Yes the system is not set to accept that. In English, if you don't use articles they seem to be adjectives, which the Klingon words are not. Can you give me an example sentence (in English is fine) where they are used in the English translation as "Terran and Klingon" and would appear in the Klingon translation as tera'gnan tlhIngan je?
It would happen most when there are a bunch of people. We are Terran and Klingon." (I picture some alien species, maybe a Cytherian, or a Talaxian, encountering the Enterprise-D Maybe he asked, Where are you from? (What species are you? could also work, but Terran is a place designation, and Human is a species.) But it could just be two. In such cases English articles would be allowed, but are not required.