Yeah Season 1 did the best with the least inaccuracies. Season 2 had the infamous "N3" rocket that was never heard from again (its a N1 in disguise?), the "Lunar" Shuttles which needed to be refueled in LEO, the Nuclear Shuttle and the Buran which were all a bit questionable but it wasn't too bad. Sea Dragon of course was a great addition.I don't know if I'm the best judge of that, but as a work of alternate history, I feel like FAM did poorly execution-wise. It has glaring inaccuracies and flights of fancy. FAM is certainly a nice show with plenty of cool concepts though.
Season 3 however had a freaking giant over-sized private Orbital space Hotel operational by 1992, then there was the Soviet Mars SSTO thing, and lastly there was the North Koreans... which doesn't need much explaining.
Still even with the flaws the show is a cool piece of Alternative history and enjoyable to watch, just ignore the fact that realism was probably lost to the vacuum of space.