I'm on my way to Colombia via the US on a C1 Transit visa, listed Detroit on my application, since that was the original travel plan.
Now, though, I am not able to go through Detroit and will go through JFK instead. Will leaving Detroit as the destination city affect my visa interview or the chances that I get approved, or should I correct it in my application?
For the most part your proposed itinerary doesn't matter. Everyone is well aware that travel plans can change (and very quickly these days).
If you have a C1 visa you can transit the US at any port of entry, unless the consulate prints a specific restriction on the visa. This is very rare though.
Note that in the US all transit is landside. This means you can leave the airport during your layover. You can also fly through multiple US airports if necessary to complete your journey. You will typically receive a 29 day admission, so you will have plenty of time in case a flight is delayed or cancelled.
