How can water enter the system once it is purged and no additional water is added?
An auto-fill valve can put more water into the system.
Or did you mean to ask how can
air enter the system?
Air can enter the system when it's under-pressurized, putting the highest elevation of the system at risk of being below the localized air pressure. It is further aggravated by negative pressures induced on the return side by pumping. Air can also enter the system from high turbulence creating very localized low pressure spots at ells and tees when pumping. This is more common in systems on 2-3 story or taller houses/buildings with the boiler in the basement. Over-pumped system with high velocity / high turbulence sections can potentially even pull air in even from vents.
I installed a LWCO. it’s electronics failed after two years and shutdown boiler. Weakest link?
Maybe. But low water isn't your problem, low pressure is. A low pressure switch is a MUCH dumber-simpler electromechanical device than a LWCO- it's a set of switch contacts, one of which is on a diaphragm that flexes only when the pressure changes.
What type of filter are you referring to?
There are any number of "magnetic boiler filters" that have both a fine screen or filter medium as well a magnetic for catching granular crap (including ferrous sludge, rust, crud) from hydronic systems. They're a "must have" for old systems using iron plumbing & radiators, not so much for stainless boilers and PEX or copper, but since your system has a history of grit problems, and (I'm assuming) a cast iron boiler it's not a bad idea to install one on your system. There are also dirt separators that use primarily gravity and a low-turbulence low- velocity chamber to allow stuff denser than water to settle to the bottom, which should take care of silica sand or chunks of rust/scale. Spirotherm, the makers of Spirovent also makes several "
Spirotrap" dirt-separator models suitable for residential systems.
It I cap the vents and there is a small residual amount of air in the system, what are the potential consequences?
If all the air collects in one spot it can form a vapor lock, with little or no flow on some branch or another. That's the primary symptom most people are concerned about, since no flow = no heat.
Air in the system will also oxidize/corrode ferrous system components (such as cast iron boilers), creating rust/crud/sludge. There may be some oxidation of the anti-freeze too.