As for the OP....Gene's worst ideas:
Most were behind the scenes. Some might say children on the Enterprise D (Justman's idea) or Wesley, etc. The irony is some of the best ideas were also the worst:
Transporters: Made the show affordable. But also made it too easy to get out of trouble=plot contrivances to get it not to work.
Wagon train to the stars/parallel planets: Using existing lot sets and costumes made the show affordable, but also made for an unfortunate familiarity and unbelievability to events, ie: Squire of Gothos, Apollo, Lincoln, Archons, etc.
Constant rewrites: Hurt the potential pool of writers. STNG struggled with this for 2 seasons, losing two bona fide SF writers in the process. Sometimes diluted the more "dangerous" scripts.
Gene's lawyer: Ok Gene was weak in his later years, but this was a huge problem behind the scenes of STNG.
Repetitive ideas: Star Trek means ideas to me, but even so too many of the scripts of TOS, Phase II(70s) and early STNG seem all too familiar. Phase II in particular seemed unimaginative.