So, this is a combination of Array and Curve.
As you can see in my picture, I've got the piece on the right selected as the cap for my array. And it works and seems to be lined up just fine.
However, if you look carefully you'll see that while my cap is shaded flat on its own, the array cap using that is shaded smooth.
Even better, if I shade smooth the array tentacle, it'll shade smooth the array and individual cap object. AND, if I undo that, and then shade smooth the cap object, it does the entire array smooth.
This is very much not a big deal (I'm mostly doing this for 3D printing, eventually) but it was a very unexpected behavior, so I thought I'd see if there's an idea as to the cause.
So, bug? Or more likely something I just don't understand the full interaction?
Blender uses the shading setting for the object that has the array modifier.
Which version of Blender are you using? Is it ok to look at the .blend file and see if I can replicate it? Perhaps using a subdiv or smooth modifier might be a better option for the cap rather than just setting it to smooth shading? Also check and see what it looks like in other viewport settings - this could be a factor of the Solid shading mode.
Using 4.2. Here you go:
https://drive.google.com/file/d/1aFAa4YRiQxI7DaivaZNI-D-ye4ot9C4d/view?usp=drive_link