Chiller AC cools some rooms but barely others — what's wrong?

The fact that some rooms are fine and others are weak is the big clue — it points to the individual fan coil unit (FCU) in the weak room, not the chilled water coming into the building. Usual suspects in that room's FCU: a clogged filter or a dirty coil choking the airflow, an airlock, or a stuck two-way valve throttling the chilled-water flow to it.

Where the line sits: everything inside your apartment (the FCUs, their filters, the thermostats) is normally your side to maintain; the building loop, pumps and supply temperature are FM's. So start with the weak room — pull and clean its filter, and if it is still weak it is worth a chiller servicing visit to check that FCU's valve and coil. Only chase FM if every room is weak at once, which is more like a barely-cooling-whole-flat supply issue.