It needed a full renovation and was very undesirable when I purchased it.

Tuxedo Park is very undesirable.

In the desire to stick to what we want (#1) and get emotional (#3), we might find ourselves with an undesirable deal.

They may not be 100% "liable" but depending on the seriousness of the issue you can believe that the authorities will drag then thru the mud before they clear them of anything.

Is probability-adjusted cost of an increase in undesirable occupants really high enough to warrant giving up $2M in valuation on a house? 

All of these point of the neighborhood having high demand and a lack of inventory, usually because the neighborhood is in transition from undesirable to up and coming. 

That TH went up $60K while it was still mud with a layer of gravel.

One of them was run by a local investor and almost fully occupied when I took over, but after I cleared out the non-payers and general undesirables, I ended up turning over 50 of 76 units, which costs $4-5K per unit.  

In addition, he has a dog and if the grass is killed this summer it will become a big mud pit this fall, winter, and spring.

If you see something undesirable, but not a deal breaker, then you will be better prepared to handle it once the acquisition is complete.4.