Is there a downside to the serum? It seems pretty much perfect.
When properly implemented, the only appreciable side effect seems to be that a) Captain America can't get drunk or high and b) his longevity means he will likely see almost everyone he loves wither away and die. One could probably argue that his great endurance and strength probably means that Steve spends most of his day feeling like he's not getting enough exercise and that he needs to go out and run a few miles or lift a few tons in much the same way that many athletes feel antsy if they don't get around to their workouts, but it seems like they give him sufficient exercise that that seldom kicks in.
Of course, the majority of cases where the Super-Soldier serum has been administered have led to body deformation, insanity, and such. Whether this is due to an imperfect process or the serum only working due to some quirk in Steve's personal build has varied over the years. Notable failures include Isaiah Bradley (brain damaged and rendered sterile), the other members of his team (deformities and rage problems), the Anti-Cap (insanity), Protocide (initially death, later insanity), Steven Burnside (insanity), and The Sentry (batshit insanity).
The Black Super Soldiers including Isaiah Bradley