The way I rate episodes is to consider if they have any redeeming value to the series in which they appear, or for the franchise in general, or for a given character (the fourth consideration is whether or not it's essential to any of the first three). Each distinction earns the episode a star.
Now, I've found a number of episodes that don't deserve any such distinction. Sometimes it's because it's not necessarily a bad episode, but that it's needlessly duplicating work other episodes have done, and really don't have anything new or interesting to say. Those are instances of Star Trek spinning its wheels. But it's more common for an episode with no star rating to have done things poorly.
The big difference between how I evaluate an episode as having done everything poorly is that I don't dock creativity if I don't happen to agree with it. For instance, "Spock's Brain" (and its descendants "Genesis," "Profit and Lace," "Threshold," and "These Are the Voyages...") is typically considered "bad" because its central premise seems ridiculous. And yet you don't have to consider it ridiculous. Free from its typical reception, the idea is actually pretty smart. If you assume Spock is exceptional, which fans tend to agree that he is, then it's not at all ridiculous that someone would show up looking to exploit him, body included or otherwise.
The point is, if the premise is truly to be considered ridiculous, and therefore an indicator of a bad episode, it should have no real shot at redemption. It doesn't say anything worthwhile to franchise, series, or character, in other words, and in fact makes any of these look about as enticing as outsiders have tended to consider Star Trek over the years.
Which is to say, barring any commentary from a fan, these are the episodes most likely to dissuade someone from liking Star Trek. Again, not completely uniformly, which is why I try to address new and old fans alike in my commentaries.
So here are the worst episodes of the franchise (as I've so far discussed):
Star Trek 2x7 "Catspaw"
The Animated Series 1x8 "The Magicks of Megas-Tu"
The Next Generation 1x4 "Code of Honor"
The Next Generation 1x8 "Justice"
The Next Generation 1x14 "Angel One"
The Next Generation 1x17 "When the Bough Breaks"
The Next Generation 1x18 "Home Soil"
The Next Generation 2x18 "Up the Long Ladder"
The Next Generation 4x17 "Night Terrors"
The Next Generation 7x14 "Sub Rosa"
Voyager 2x6 "Twisted"
Voyager 3x24 "Displaced"
Voyager 4x10 "Random Thoughts"
Voyager 6x14 "Memorial"