One of the units does have a minor infestation of brown wood cockroaches, but since they haven't spread to the other units, I'm hopeful they won't be too difficult to exterminate.

I ordered a 3rd party inspection and a list of items came back that needs to be (leaking pipe under sink, rodent infestation in the attic, downspout that needs securing, sewer vent pipe out to the attic, missing smoke detectors in a unit, loose material from basement wall which can compromise foundation if not fixed, etc...).

The landlord knocked on one door to collect the rent and the tenant broke his nose and said, I told you not to come again for the rent".We had the housing authority (if that is what it was called it at the time) on our butts every day because the tenants would break window screens, break door locks, keep their apartments filthy so they were infested with roaches and rats and we could not keep up with repairs.

Somehow this invasive species causes property values to increase after an infestation.

I plan on installing some form of termite protection after purchasing anyway, but is there anyway to make sure I'm not buying a house with a full blown infestation that could become a bigger issue?

However, if the furniture is infested, you probably need to replace affected mattresses and couches.

And an infestation of German roaches that made the pest guy jump (he said).After everything was said and done, we incurred 4 times the cost as I was told/ estimated. 

There is also a bedbug infestation there.  

In our case, my wife and I could afford a run-down fourplex that needed extensive work and was infested with roaches.

But as previously mentioned - if you didn't know the roof was rotten, and the inside is completely mold infested because of leaks, you could quickly be in for way more money than you expected and you could lose money if your repair costs exceed the value of the property, for instance.Liens work on the basis of seniority.