Off the top of my head:
- Glass making. Probably the biggest single one. Without large glass windows neither the Roman baths nor most of the Roman palaces work/can be heated. Guess why most early medieval churches have small windows, if any at all. Heck, even simple Roman houses had glass windows.
- Use of water in specialized mills. Like
this one. One single mill avaiblable to satisfy up to 30.000 people per day. That is the true Roman genius.
- Mining and iron production, both scale (nearly global production, on levels not reached until the 1800s again) and technology. In some areas there was no iron mining despite deposits until the 1800s because if you needed iron, just crack open a roman building and rip the iron out of the walls. Heck, in Greece I know people whose wedding gold was "freshly" procured from Roman tombs in the area.
- Roman specialized concrete - standard concrete still existed, but the specialized concrete for underwater harbour construction etc.
- Architectural knowledge, like how to construct a bridge that will stand for centuries without moving or breaking apart. See
this for the most striking example. Look at the picture. See those breakwaters at the front to prevent winter ice from crushing the bridge? Something that was not built again until the high middle ages. Also, note what those breakwaters are made of. Black stone, (iirc Basalt) because unlike other stone, it will not gradually suffer from water erosion etc. And the Romans transported the whole stones from far aways just to build a bridge that holds.
Even today the orignal foundations still hold cars and trucks. Think about that.
A bridge that was build over 2000 years ago is still carrying trucks and cars today. While serving as a direct access point to a highway and being probably being one of the three big ways into one of the largest German cities today. Do you feel comfortable saying that about today's bridge construction?
- More architectural knowledge and institutions, like road maintenance and road construction
- Specialized fishing and transportation technology aka "how do I transport living seawater fish from Great Britain all the way to Rome without spoiling it". Something we need refrigerators for, but which the Romans did regularly and with ease.
- Specialized nautical institutions and technology. Like Lighthouse constructions, using a comprehensive signal system, keeping logs of obstacles empire-wide....heck even something as simple as a road travel map encompassing all of Europe.
- A system of taxation that made long-range trade possible and plannable
- Sound engineering. Sounds trivial at first. But consider - there were no microphones. Yet if I stand in the middle of a Roman amphitheater and just speak normally, even those in the upper ranks can hear me. If I raise my voice, it will easily cut through crowd noise. (I am not pulling a leg, I've tried this multiple times). Compare this to the pitiful sound engineering in, say, churches of the Carolingian times, where it is most likely just flailing around like "MUST HAVE ABSIS. ABSIS GOOD FOR SOUND."
But most importantly, the complex super-regional economical trade or resource exploitation. Look at a Roman city. Here is what it needs:
- Vast amounts of firewood, if only for the Thermae. Lower Germany is reckoned to be nearly entirely deforested due to the appetites of those Thermae, especially those at Cologne and Trier. One could not do that in the middle age due to loss of available workers as well as the fracturing of the political landscaep.
- Vast amounts of Grain, in some cases exported halfway around the known world. Also vast amounts of specialized foodstuffs (olive oil, garum, oysters etc.) that make Roman life possible but which also need safe routes of travel and lots of workers.
- Vast amounts of Iron, lime, stones and marble for building. Not possible due to the above-mentioned restrictions.
- Clean water. Records show that the average Roman in a city like Trier used from 120-200 liters of fresh water per day. We Germans today use less than that and that is with industrialization etc. To have such water, you need an aquaduct. How do you build an aquaeduct?
Well, you need to keep the exact degree of down angle for distances of up to hundreds of kilometers. Exactly the same or the whole aquaeduct is useless. You also need to build the thing simultaneously in several locations (or you will never finish) and hope the pieces do match when fit together. The amount of planning and engineering that must have gone into those, especially in the hilly/rocky terrain of Italy and lower Germany...Oh, and you have to clean them from sediment every decade. (Fun fact: In the middle ages those sediments had by then turned into a soft, easily cuttable stone and were sold as valuable ornament materials all over Europe. Nearly every palace of that time has this sort of stone, most often used for figures or arches.)
All those things are what made Roman life possible. Remove any single one of them and the system collapses or loses the things which made it Roman.
I always considered the comparable high standard of life and technology, which easily was centuries ahead of all the Rest of Europe until the tall end of the Renaissance (and only then concerning Northern Italy), the most impressive feat of the Romans, much more impressive than all their military prowess combined. Heck, Roman sound engineering is still not matched in today's sports arenas.