You'll want to fill in all the seams. While the vertical ones MAY be where various hull sections meet (I don't know), it doesn't matter, because the entire hull is covered with tiles and so you can't see any of those seams.
The Tucson is the SSN 770, and is therefore one of the Improved LA Class. You'll need the stuff on the sprue "D" to build her. To do it correctly, you'll need to revise the locations of the tomahawk missle hatches (add two and fill in two), and use the small rectangular planes for the front of the hull. I filled in the holes, did a lot of filling and sanding and then went back in later and added the hole to insert the planes.
Additionally, you should probably scratch build the two pods on the stern where the decoys are deployed. I know that Columbus (SSN 762) and Boise (SSN 764) had them, and I suspect that all subsequent boats were built that way as well. And they've got the shape of the sail wrong as well, it's flatter on top and a lot more blunt/rounded on the front end compared to the back.
One final touch would be to add a circular shroud around the outside of the prop.
You will have a difficult time finding pictures because the Navy doesn't like people to see what it looks like back there. (But I've got some shots in my gallery

)
My son spent two years on each of the two boats mentioned and provided a LOT of good advice on how to correct the kit.
I'll be happy to answer any questions you have.
Tom