To name a few,
Season Two's final episode, "Assignment: Earth". Imagine if the series didn't get renewed for a season three and Assignment: Earth ended up as the original series' last episode. Quite an insult when you consider that it wasn't meant to be a Star Trek episode at all, since Gene made it as an attempt to get a new series started by using Star Trek to make this backdoor pilot.
The Star Trek theme. Gene, as long as your lyrics don't appear in the theme, I will never, EVER credit you for creating the theme. You did not do this to make the theme better, you did just to rip off Alexander Courage. Practice what you preach.
Treatment of women. Sorry, but I don't like a sexist Starfleet, or your idea that a woman who isn't pretty can't have a future. Plus writing that one line "They're like animals" to describe a green skinned woman dancing to music is just bad.
Wesley Crusher. If I was a child actor and I learned years later just how much Gene Roddeberry was attached to Wesley as a character, I would feel almost violated. Think about it. The whole point of Wesley's character was to fulfill some old guy's self-important ego. Ick!
Canon. Oh, for god's sake Gene. It's a story written by a writer endorsed by the studio with your name on it. Just because it's not on film doesn't mean it's not a story worthy to be acknowledged.
Killing Tasha Yar. This could have been handled a whole let better Gene. A LOT BETTER.