Translation:The captain complained that the airplane is not clean.
Yes. It should be: The captain complained that the plane was not clean. It is so called consecutio temporum. https://en.m.wikipedia.org/wiki/Sequence_of_tenses
The dependent clause should also be in the past tense in English. It is not impossible to use the present tense, but it would have a specific different meaning (that the plane at present is dirty, the captain has already made his complaint, but no one has cleaned it yet). With the past tense, it has the more natural meaning that the plane was dirty at some time in the past, and at that time, the captain complained. If I'm not mistaken, in Hebrew, the lack of any verb implies simultaneity to the main clause. This would correspond to the English past tense subordinate to another past tense, which also implies simultaneity.
I'm in total agreement with those saying the English translation is incorrect. While it might be fine in Hebrew to mix tenses like this, in English it should read 'that the plane was not clean.' As JoshRodrig17 explained, there might be contexts in which 'that the plane is not clean' would be correct, it is far more common and natural in English to use the past tense in the second part of the sentence as well. It is still being marked as incorrect (October 5 2018).
Look, the word for captain is an old loan from Greek κυβερνήτης [kybernetes], קַבַּרְנִיט. The last t of kybernetes is part of the stem in Hebrew and is written as usually in such loan words with a ט. But the feminine ending for professions in Hebrew is ית with a ת. So the female captain of a ship would be a קַבַּרְנִיטִית.