Address the leak immediately, once the house is water tight get everything dry and then you can approach the cosmetic repairs over time. 

Restoration company, with a $500 deductible for home insurance, is drying and working on fixing tile that is water damaged, grout that has eroded, drywall that needs replaced, etc etc.We have about a dozen examples of issues similar to this.

I realized that carpets were completely dried and called restoration guy to remove them if not required.

Just kidding, this thread is too martini-dry.  

Don't get super aggressive where you run dry of cash or put yourself in a pinch.

I can’t imagine it ever drying out if it did.

Personal liquidity and some "dry powder"2,500,000 - Quicker Return Investments.

This may result from slipping on a rotted stair, or tripping over the water sprinkler, which may or may not be the fault of the landlord to begin with, depending on the terms of the lease.

I’ve replaced rot pretty much everywhere but that.

But 90% do and as stated our dry wall contractor is one the hook for those and our touch up paint year one is included in my contract with my painter.