In these markets, I would be worried about crime, activity of illegal immigrants, and such. 

No free lunch in this market!

Let's assume that the neighborhood is a C class and the median income of the city is greater than 3X of the market rent.Here are some of the considerations I've come up with so far:- Units are in need of renovation and capex is too high or not available- Unit quality is not the same as market - Seller is worried about losing tenants due to increase- Vacancy rates are high or filling units have been difficult- Rent increase would take multiple increases over multiple lease periods to get to market rate if seller is trying to retain the same tenant- Seller inherited property and just want to liquidate- Seller needs to liquidate quickly (financial burden, sickness, quick exit from land-lording)It seems like I might be missing a warning sign about a deal if they are selling with current rents that are under market; but again, this seems to be most of the properties I've underwritten.And in the same vein, what should I be worried about when purchasing a deal with under market rent with the intention of raising them after purchase. 

If you and your wife are on the same page, I say absolutely go for it.Don't worry about the naysayers telling you to invest out of state if that's not something you're comfortable with right now.

i would not worry about this threat at all.  

Haven't had any issues, but I am worried about liability should something happen like a fire. 

They'll roll up good reviews quickly and organically.Don't worry about manufacturing reviews.

And. if you have a property management question along the way, feel free to reach out to me. 

if you are worried about vacancy, then multi-family is what you should go for.

If you set it up well, don't worry, you'll get guests when you repost.If you really want to capture the existing bookings, then go for it and plan to re-furnish it at the start of slow season.