I already have one, and I'm not sure if I'm putting this in the right place. If I am, sorry, move or delete if you must. My question is, if I got them to breed... would the offspring do anything freaky to the family tree over time? Are there any bugs or problematic issues that can arise? Just curious.
I want to know whether my twincest couple should make a baby or whether it is something I should avoid.

The only way to find out is to make a test neighborhood and try it. If you're pairing siblings, that shouldn't do anything strange to the family tree at all - the baby should just have mother/father links like normal. And since the genetics only pull face structure, skin, hair, and eye color from the parents it's not like there would be serious health consequences as you'd see in real life.

I tried this once, not with a mod but with InSIM. No visible issues, but that was before I knew about hood corruption. I can tell you that the game ran just fine for another two generations, with no signs for corruption. And seeing as I was trying to recreate Anne Rice's Mayfair Witches, that should say something about the stability. ;-)

The family tree will look a bit weird, you'll see the kid twice if you click on the grandparents for example. The kid itself only had one parent in the family tree, which I couldn't change with InSIM. This is probably because the game couldn't display the child being its own sibling. This is probably the only risky part, it might create duplicates of your sims. You should check for that in the test neighborhood.

It won't - the family tree only displays portrait pictures, not actual sims.

Okay, that's good to know. I thought I'd read somewhere that it might cause problems, but never got to test it. Seems safe-ish to me then.

I manage to manipulate the lineage so a lot of 8 sims were related to each other similar to the bartender paradox
4 generations
A and B are siblings, they had C and D.
C and D had E and F
E and F had G and H
G and H had A and B

Every Sim in that tree is their own Great Great Grandparent
or put another way their grandparents are also their grandchildren.

No corruption was caused by this, and did show two portraits of their Grandchildren/grandparents. both up at the top of the tree and at the bottom.

talk about incest!

Have you seen the Smith-Curious family tree? Anyway, this isn't real life, so you shouldn't have any problems other than maybe a weird family tree.

Somehow it reminds me of "I'm my own Grandpa".