I started to make a post on concepts from Trek lore that I thought were as problematic as time travel (no money, post-scarcity economics, the holodeck...) but the list expanded so quickly that I had to stop.
I think maybe what a Trek game really needs (and sf games in general) is a meta-system for managing and controlling which game-breaking concepts are in play. I mean, time travel, transporters, replicators, the holodeck, the Genesis device, the list goes on.
That way, if you want to expand on what a piece of Treknology does, you have to pay points for it, and maybe give up other shiny objects.
"I want to have the implant translator function as a comlink." "Do you have the McGuffin points for that?"
"I want phasers to have a stasis field setting, and I have enough McGuffin points to activate it as a one time only effect."