prefixes - Rule to determine when to use the prefix "im" vs. "un" to negate a word starting with "p"?

Simchona linked a good reference, but I do see a small difference in the examples you listed.

Polluted, polished, and plugged are all results of physical actions. Plausible, possible, and perfect are all conditions, or adjectives. It makes sense to me that they would be negated differently.

Done - Undone
Spent - Unspent
Paid - Unpaid
Pinned - Unpinned
Hinged - Unhinged

Proper - Improper
Movable - Immovable
Balanced - Imbalanced
Material - Immaterial
Measurable - Immeasurable