Learn Farsi: انتصاب وزیر جدید یک اشتباه بزرگ بود. - The appointment of the new minister was a big mistake.

The Arabic root is n-s-b (ن-ص-ب), which relates to setting up or fixing. By applying the e-C1-t-e-C2-â-C3 pattern, we insert a t after the first root letter and lengthen the vowel before the last. This forms e-n-t-e-s-â-b (انتصاب), giving us the resultant abstract noun 'appointment' (setting someone up in a role).

I know eshtebâh means 'mistake,' but is it actually a Form VIII noun too?

Yes, it perfectly follows the pattern! The root is sh-b-h (ش-ب-ه), which carries the core meaning of resembling or being doubtful. When you plug those consonants into the e-C1-t-e-C2-â-C3 structure, you get e-sh-t-e-b-â-h (اشتباه). The meaning shifts from 'doubt/resemblance' to the resulting 'confusion' or 'mistake.'

Why is yek (one/a) used here instead of the indefinite -i suffix on the word for mistake?

In Farsi, you can express 'a/an' by placing yek before the noun phrase, adding the -i suffix to the end of it, or using both simultaneously. Here, yek simply functions as a standalone determiner for eshtebâh-e bozorg. Both methods are grammatically correct, though using just yek or both together can sometimes add a slight emphasis to the singular quantity.

Why isn't there an Ezafe connecting the subject phrase ending in jadid and the next word yek?

(the appointment of the new minister) forms the complete subject of the sentence, while (was a big mistake) is the predicate. You only use an Ezafe to link words within a phrase; you never use an Ezafe to connect a subject to its predicate.