I am trying to take over a factory I built awhile back but every time I try to attack it, it says "limited engagement" and won't take the place over. There are no enemy units on the tile it says I am bombarding it, and the factory is taking 0 damage.

Which unit are you using to conquer the city?

Undetected sub. See post from before.
Sub in city immune to all except naval -> you can modify targeting dat or bring some unit with naval attack or psy to get rid.
Wonder why anchored ships count as naval at all.

ya it was a sub I sent a destroyer from a different factory and was able to take it over, had to have a army there taking out whatever they built for a few turns though.