I'm trying to figure out the kind of setting Battletech takes place in.
To be honest, it's changed over time...back when the game first came out, there were no 'Mech manufacturers, and all the "factories" were actually more akin to spare parts warehouses, constantly being fought over to keep centuries old machines functioning...hence the phrase: "Life is cheap. BattleMechs aren't."
Needless to say, the developers realized that if the game was going to continue and grow, this kind of setting needed to be able to do so as well...therefore, it was altered. It became such that there was manufacturing, even of 'Mechs and JumpShips, but barely at a rate that kept up with normal losses during the Third Succession War. Advancement was limited both due to limits on communication between scientists, but also because that self-same communication was being handled through an agency that was actually working against the powers that be in the Inner Sphere to keep the tech base low. That agency also would kidnap select scientists or covertly destroy research made by the nations of the Inner Sphere to keep them relatively low tech. This agency was, of course, Comstar.
But this only lasted so long as well, and discoveries were made that allowed some of the old Star League tech and manufacturing capabilities to be restored, which started a domino effect similar to the Industrial Revolution, in which one discovery or invention led to another led to another led to another. And this was needed as the Fourth Succession War and the War of 3039 presented warfare on a scale not seen in the Inner Sphere in over a century. Which was fortunate because in 3049, the Clans arrived, again changing the nature of warfare in the Inner Sphere. The Clans drove even more advancement in the Inner Sphere, in some ways superior to that of the Star League, and eventually even WarShip manufacturing became possible again.
But human nature being what it is, certain parts of humanity worked to control and/or destroy the rest, and the WoB Jihad and the Wars of Reaving took place, obliterating much of what had been gained, but not quite on the scale that occurred during the First and Second Succession Wars. This left some of what had been gained still functional, and for a time brought a relatively peaceful time to the Inner Sphere (in comparison to what had just occurred in the previous 75 years), although even then, there were still border skirmishes and wars.
As the time approached 3150, new factions formed, or took control of what already existed...factions that felt they have the right to rule or destroy what others have, and a new spectre of war and destruction has again descended upon the Inner Sphere...
Edit: Or to answer your original question more succinctly, when the game first came out, there was little to no real scientific knowledge at all. What was kept and maintained was done basically by rote (ie, the fixed things the way they had been taught, and hardly any, if any at all, new advances were being made). Then the game was changed such that, yes, they did fully understand tech and science at least to the late 20th century level or into a 21st century understanding (as the 21st century was seen by those in the 1980's), and then change again so that new things, whether they be in weapons, defenses or other fields of endeavor, were being made at a decent rate.
Ruger