In "The Host," Odan can't use transporters, The Federation doesn't know anything about his race, and the Trill wear standard, nose-based appliances. In Deep Space Nine, Dax uses transporters all the damned time, she negotiated the Khitomer Accords as a member of The Federation, and she's just a pretty human with spots.
Star Trek is full o' this shit:
Now, I say most of the legitimate inconsistencies come from Star Trek VI getting ignored by everything that came after it and the makers of The Next Generation movies ignoring everything that came before them.
Now, I'm not a big fan of continuity. It's necessary for building character and Deep Space Nine used it to great effect, but it's nothing to get hung up on. Tell a story first, then if you can fit in some continuity go right ahead.
Therefore, I'd like to introduce the USS Merlin. According to the non-canon Memory Beta, Merlin is an Akira-class vessel from one of the video games. It doesn't matter; it could be a freighter from the 23rd Century and it would serve the same function.
You see, Merlin is a quiet little ship that performs its patrols and boasts a marginally competent crew. They really do mean well but things keep happening. Temporal things.
After the first incident, they thought they hadn't caused any trouble. It was only a few months later that they realized humans were had latent telepathic abilities. The command crew panicked, recreated the accident, and tried to set history right. They screwed up and when they came back, The Klingons were...different.
They realized fixing things was more trouble than it was worth. They reported their actions, accepted their reprimands, and went about their business.
Then something else happened. A temporal vortex or something. Whatever. When they returned, the history of Romulan relations with The Federation had changed. They again reported themselves, but it turns out it was their first offense; the earlier reprimand didn't exist. As time went on, they found numerous, smaller changes. A Ferengi idiot suddenly became a savant. Cybernetic design principles changed. The Klingon thing changed again.
And then it happened again, except they'd changed the timeline so much they belonged a century earlier. Everyone else was mostly the same (family, friends, history) but adapted to the new timeline. Just as they came to grips with that, another anomaly happened by (maybe a singularity undergoing a spontaneous polarity reversal. Whatever.).
And so on. Pretty soon, it became commonplace for the crew to travel through time and they got pretty good at noticing the changes. Sometimes, they would even pick up on timeline alterations from other sources. It did make the annual retraining related to preserving the timeline awkward.
So, if you're ever watching Star Trek and something doesn't quite match up, just think of the poor crew of the USS Merlin and how much trouble they're trying to stay out of and just remember...
...a wizard did it.