Learn Spanish (Spain): Fue un simple error del político. - It was a mere error of the politician.

This is a case where adjective placement changes the meaning. When simple comes before the noun, it means mere (a mere error). If it were placed after the noun, like in un error simple, it would mean the error itself was uncomplicated or easy to fix.

Why use the preterite fue here instead of the imperfect era?

Fue (from ser) is used because the speaker is stating a completed fact about a specific event in the past. If they used era, it would sound more like they were setting the scene or describing an ongoing background situation.

Does the adjective simple change if the noun is feminine?

No. Adjectives that end in -e in Spanish, like simple, are the same for both masculine and feminine nouns. However, they do still change for plural nouns, so if it were multiple errors, it would be unos simples errores.

I have seen político used to mean political. How do we know it means politician here?

Político can be either an adjective (political) or a noun (politician). You can tell it is a noun here because it is preceded by the article el (hidden inside the contraction del, which is de plus el), making it mean of the politician.