There is no running water, the plumbing would need to be redone. 

HVAC duct work insulation is also deteriorated.No vapor barriers installed eitherSome fungi/mold growth notedPlumbingMultiple small leaks under sinks and from bathtub and toilets.House has Polybutylene plastic plumbing which is dangerousMain shut off valve is damagedElecticalSome small exposed wiring and bad splicing.Whole house has no GFCI's or grounding outletsInteriorMoisture spots on ceilingExteriorLose Vinyl SidingDoor Jams and Window trim have moisture damageDriveway need replacementRoofingMinor leaks noted in atticRecommended to replace roof covering, but not whole roofSome fungi growth noted in roofSo some of the question I am trying to tackle with this work is:How much should I budget for the main issues listed? 

I'm the landlord of a 3-unit building and wanted to know if I should be concerned about any potential plumbing issues (like freezing pipes) or other safety concerns.What steps should I take to protect the building, and are there any other things I should be worried about in this situation?

Because of their experience, I was able to get parts of the work covered under code upgrades for things that I did not build back exactly as they were before the claim (e.g. moving plumbing to expand a bathroom).At the end of the day, no one is going to care more about your property than you.

Without the sprinkler permit you can't pull an underground plumbing nor interior plumbing permit and if you're amending the plans that could hold up both of those permits, which could stop your build in its tracks, depending on when the mistake is caught. 

Hey @Devin Bost, I would highly recommend a few things to help with this. 1) Have systems and processes lined out for any emergency you can think of.2) A spreadsheet of subcontractors/ vendors that could handle the situation that arises (plumbing leak, electric out somewhere, etc.)3) Your cleaning team and handy person should be utilized for some things.4) Something like Breezeway can give you 24/7 support around your property with a dedicated phone number line.

The only things you need are the dimensions, photos of the plumbing, and a budget.

We did use a high-grade vinyl plank flooring over the concrete floor down there, just in case, but years later we can say there have been no more water issues.We also plumbed in and installed a laundry room, purchasing twin pairs of coin-op Speed Queens.All of those renovations allowed us to go up-market a bit, from the prior $160/week to $180/week within the first few weeks on the incremental rehabbed units.

I had to redo the bathrooms as well and dealing with old crappy plumbing was not fun.

They installed bidets without my permission and created plumbing issues so I had to pay for a plumber to come out several times, I've had to replace a frontdoor knob and deadbolt last month even after we rekeyed the home prior to them moving in, the garbage disposal blades were jammed so had to call a handyman, repaired a broken window which my property manager claims was broken prior to them moving in even though the repair was made 3 months after they moved in.