A few things to remember about a believable future.
Problems are solved, new problems develop.
If people don't need money, people will still crave power or adventure or a new vice or just plain danger. People may not need jobs, but they need to do something. Even if it's roleplaying. 
Although computers would probably be implantable by then, you might still want computers to have terminals (although voice activated) and be as annoying as their 20th century counterpart. Why? Because, it's different, yet familar. If computer problems don't exist in 27th century, it won't be believable. However, the things you can do with a 27th century computer should be impressive since everything is connected and probably on-line (even if it shouldn't).
Medicine will be different. Things that were incurable now are waved away with a simple shot. You will still need to be looked at by a doctor who will scan you, look at the numbers and tell you to come back in about a year. Even though it's a 1/100000 chance that you will develop anything worth worrying about. (Unless you are a PC playing with experimental stuff)
If replicators exist, make sure you know what limits them. Else everyday will be Christmas with an electronic Santa building everything for the PCs. You can be rude and give them an amazing replicator bill at the end of the month. "Replications aren't free."
OR make sure that anything of value can't be replicated. Especially computers, replicators, certain starship parts. Stuff that can't be replicated (for any reason) will be valuable.
"One of the hardest things to do, as a GM, is to make simple fantasy economics work. That's because it is easy to imagine flying dragons and magic, but simple economies that work, that is truly beyond even our wildest fantasies."
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