Just make it a habit of checking it daily or create an alert for RE with an email address.FSBO (for sale by owners) is another way to get deals.

Each room area has to have a minimum habitable space.

Make sure you have your own inspections done and find a good PMC to give you their opinion BEFORE you buy.You might want to read our series about “How to Screen a PMC Better than a Tenant”, since selecting the wrong PMC is usually more harmful than selecting a bad tenant: https://www.biggerpockets.com/member-blogs/3094/91877-how-to-screen-a-pmc-better-than-a-tenant-part-1-services-and-processes

It's clear that the house is at least habitable, as it has several people living there now.

In Texas, if the original owners want to redeem the property, they must pay 125% of the tax sale amount in the first year, or 150% of the tax sale amount in the 2nd year, plus any maintenance costs required to keep the property habitable. 

I'm specifically looking for dumpy multi-family homes that are going for a steal, but still habitable.

Don't get cute, and damage the relationship if it's good or harm your business. 7 days without AC in Texas is brutal.

We don’t know any PMCs to recommend in the area mentioned, but since selecting the wrong PMC is usually more harmful than selecting a bad tenant, you might want to read our series about “How to Screen a PMC Better than a Tenant”:https://www.biggerpockets.com/member-blogs/3094/91877-how-to-screen-a-pmc-better-than-a-tenant-part-1-services-and-processesWe recommend you get management contracts from several PMCs and compare the services they cover and, more importantly, what they each DO NOT cover.

We don’t know any PMCs to recommend in the area mentioned, but since selecting the wrong PMC is usually more harmful than selecting a bad tenant, you might want to read our series about “How to Screen a PMC Better than a Tenant”:https://www.biggerpockets.com/member-blogs/3094/91877-how-to-screen-a-pmc-better-than-a-tenant-part-1-services-and-processesWe recommend you get management contracts from several PMCs and compare the services they cover and, more importantly, what they each DO NOT cover.

In most places heating is required for a dwelling to be considered habitable, and you'll probably get a lot better tenants if you have AC in Jacksonville as well to mention that it should help keep mold at bay better than nothing, If I were you I'd cough up the money to put in a new HVAC system.