There are multiple possible improvements for moving the coolant, in pumping systems. There are piezoelectric pump and electrohydrodynamic pumping systems being worked on, with main advantage being increased reliability. One other candidate would be thermoelectric aka Peltier effect pumps. Similar tech would have ample applications in terrestrial cooling solutions.
You can find state of the art and proposed future solutions discussion in NASA technology roadmaps, for this it is the technology area 14, thermal management systems.
There have been multiple different issues with the external ammonia cooling loops, from what I understand. Two that I know of was a pump failure, that had several contributing causes. Pump was returned to earth and taken apart. Basically operating conditions pushed several components (bearings, seals) of the mechanical pump outside of the design margins, resulting in wear. There are also issues with valve failures inside PVTCS, which I don't think has been fully root-caused. In each instance, contributing causes have been mechanical complex systems that are quite hard to get right on orbit, even though electronics failures have been suspected.
At a very high level, the possible mitigations are iterating and improving the mechanical subsystems, by understanding the operating conditions better one can design better margins, use better materials and subassembly designs etc.
The other possible mitigation is to try and minimize moving parts as much as possible and use solid state systems where possible. That's where the future currently TRL 3-4 level technologies come in, mentioned above.
There have been a plethora of operational lessons as well of course. Ability to return failed subsystems to earth for quick analysis and design improvements is a key one, as the best way to improve technology is still to operate it and learn from the process.