This is really a question of personal style. You can omit any repeated words in a sentence, as long as it doesn't make the sentence harder to understand. Your second example is fine, but why repeat "inappropriate" three times? Once is enough. Also, the first "the" is optional.
We also exploit (the) inappropriate relevants, searches, and queries, as well as the publication-date-based filtering heuristics.
However, sometimes you want to repeat words for emphasis.
When visiting the courthouse, students must refrain from any disruptive behavior. No loud conversation, no loud laughter, no loud music, no use of cell phones, no unnecessary fidgeting, and no chewing gum.
You should not remove "the" when it is an expected part of the name of a place.
While visiting New York City, we plan to go to the Statue of Liberty, the Empire State Building, and the United Nations building.