What you've shown here is not really a cause for concern in my eyes, however I see much worst conditions regularly.

Anything I need to keep an eye out for?

Most home warranty policies would cover leaks.As far as what is acceptable, in my market (Milwaukee) nobody bats an eye on cast iron sewer pipes or clay tile sewer lateral.

No one blinked an eye!  

If these are the only ways that you can see to make small multifamily work right now then you need to take off your blinders, eye patch, sunglasses, or what else might be impairing your vision.

I did walk away basically breaking even (probably out a few grand, but not losing my shirt) and with a much better respect and eye for a "great deal." 

Look for cracks in the foundation, walls, or ceilings, as these may suggest settling or shifting.Additionally, keep an eye out for pest infestations, particularly termites or carpenter ants, which can cause significant damage to wooden structures.Lastly, be aware of environmental concerns such as radon levels and underground oil tanks, which can pose health risks.Having a qualified home inspector conduct a thorough evaluation is essential.

This allowed us to get many eyes on the property, which was a game-changer.

I’ve learned to start the permitting process early and keep a close eye on inspection timelines to avoid bottlenecks.It can be difficult to find contractors who are not only skilled but also reliable and available when you need them.

Speaking from a property manager's point of view, unless you can have eyes on your property at least once a year, you should not be self-managing.