Nothing in the video about drone use, though I saw one bit where they're launching on the other side of the Arno river, so curious how much footage of Florence they got and whether they were hassled anywhere for launching and landing drones, especially anywhere near the town centers.
I would assume for instance if a drone circled around those famous towers or cathedrals, there would be objections.
As for the tips themselves, yes wifi is poor but Italy has good Internet infrastructure. It just depends on whether the Airbnb owner decided to pay for good speeds. I returned from a stay at a Bari Airbnb and speeds were over 100 Mbps and never had any problems.
I do stay in hotels though. For instance, I checked Airbnb for Siena and Ortisei, which both have high hotel prices. But apartments weren't a lot cheaper, though there would be more room usually. Hotels in general don't have fast Wifi. They have to share a connection for the home market or they pay someone to manage the connection so it's slow. It's not better at the big international chains because a lot of them will give you slow Wifi for free and then upsell "business class" Wifi which isn't that fast for more money.
In Italy, they have GREAT mobile networks so I usually buy a SIM for 20-30 Euros and get great 4G speeds and coverage. I use it in hotels if the speeds are really bad. Otherwise, you can burn through 10 GB in a night of streaming.
Anyways, from the few shots in the video, it looks like the OP had no problems using drones all over. I think that would be more true in the countryside but not in actual bigger towns, especially over the center, unless you want to fly FPV and take off and land a kilometer away and high enough to avoid detection.
I had some disconnection problems in a recent trip in the Amalfi Coast and Capri so I didn't get to fly as much and I'd be scary to fly over crowded towns only to get it disconnected and fall over crowds.