From the first episode on I wasn't too sure what to make of this show.
Somehow, the story was compelling and intriguing, otherwise I wouldn't have tried this but the actors were mediocre for the most part.

After hanging on and having watched 8 episodes now, I do like the cast much more but the cliché roles are still way too apparent and over time new ones were added.
The main premise was about a little girl of 3 years, being abducted by another person who raised her and is now taken away from her, the now teenage girl is returning to the biological family.
This premise, the main story, more and more goes into the background and instead the episodes are dealing with slice of life stuff, more often than not independent to the premise.
Being a fan of Gilmore Girls this isn't too bad and you could argue it is for Carter to find her way in to the everyday life of a "working" family but it seems like a waste for this at first intriguing story most of the time.
And just like similar shows this show suffers from the main character as the main source for all kinds of absurd(!) problems all around her, her being the only person who can and will solve those problems of anyone else except her own, with the world only spinning around her. In this case, of course, Carter.

The directing is good in general, though, the cast is so and so, some bad ones are here, too (Lori, the abductor, is awfully bad but I rather blame the script here than the actor), nothing extraordinary but charming.
When you liked Gilmore Girls you might like this, too.
But as it is often mentioned, I agree that Finding Carter runs on the wrong network and with that tries waaay too hard to appeal to a younger audience than necessary (hence called "teen" drama) for this kind of premise. Including with way too young (looking) actors on average.
You could get so much more out of this on another network.