I'm a software engineer with a Physics/Maths degree, and although I say it bothers me, it doesn't bother me enough to stop watching. For instance, I'm bothered that so many Star Trek episodes were cleared up in the last five minutes by "recalibrating the sensors", or that they have Inertial Dampeners that prevent them from being smooshed to an atom-thick soup on the back wall when accelerating to FTL but the dampeners can't handle a little bit of shaking (at least install seat belts) - but what really bothers me about Star Trek is that the Prime Directive can never be broken except when it's expedient to do so for this week's episode. The magical science hasn't stopped me watching Star Trek.
Or The 100. When they showed the space habitat for the first time, with multiple rings rotating at different angles and some parts not rotating at all, I thought "the stresses on the frame must be tremendous, how does it not break apart?" but I only stopped watching after they killed off Lexa.
However, there are thousands if not millions of nerds out there who would be happy to help writers get the science right. Too much of it is just sloppy writing, trying to get a dramatic effect that lasts five seconds based on something that makes no sense. Saying "most people won't even notice" isn't an excuse. It can be right and have dramatic impact.
By the way, the thing that bothered me most about the last episode of For All Mankind was when they showed Tracey's grave and it said Medal of Honor winner, but Tracey wasn't military personnel. I know civilians have won the Medal of Honor, but not since the Civil War.