I'm not overly interested in purchasing properties and having to deal with tenants, broken toilets, etc. - my day job keeps me pretty busy.  

They know how to get deals, renovate, push equity, screen tenants and manage.

You may have the tenant on a technicality in that they didn't report the broken disposal and can't claim they didn't have time since they had time to pack their belongings and move out.

When a guest calls because the door lock is broken, I have to pay our person to 1) Travel to the site to assess, 2) Go to Lowe's or HD for the part, 3) Return to the site, 4) install the part, 5) travel back home.In the mountains of Tennessee, that can be a 4 or 5-hour process really easily. 

Honestly, the screening part is the worst and effectively demands landlords violate fair housing by requiring that you evaluate things like evictions "holistically" (i.e. preventing landlords from having consistent policies that treat each applicant the same.That being said, the bill is better than the original version at least.

Now that the rehab is complete, there's some equity in the property, and I'm moving in, I can't help but wonder if it's smart to take this time to do something on the side to pay down my mortgage faster or start educating myself on screening tenants and doing my due diligence.

To mitigate this risk without using an LLC, consider:Umbrella Insurance: This provides additional liability coverage beyond your standard homeowners insurance.Equity Stripping: This involves placing a lien on the property to make it less attractive to potential creditors.Land Trusts: These can provide some anonymity and protection while allowing you to maintain personal ownership.Insurance:Ensure you have comprehensive insurance coverage, including:Property insuranceLiability insuranceFlood insurance (especially important in Florida)Loss of income insuranceLegal Structures:While you've decided against using an LLC, consider consulting with a local attorney specializing in real estate investments to explore other potential legal structures that might offer protection without the tax implications you're trying to avoid.Property Management:Given that you're based in Europe, consider hiring a professional property management company to handle day-to-day operations, tenant screening, and maintenance issues.Market Research:Thoroughly research the specific areas in Florida where you plan to invest.

Drainage pipe is broken/clogged somewhere and water drains freely under the driveway.

Would it be maintenance requests, tenant screening, lease management, or something else?

Its all about screening and having a good team in place.