Are there infinite side-quests in Fallout 4?

Yes, it does; I have been doing mission after mission for the Minutemen. They sometime send me back to the same place. Its actually kind of nice.

I've been doing a fair amount of missions for the brotherhood of steel, and it LOOKS infinite ; i've collected something like 20 tech pieces and cleaned about 15 areas for those two NPCs, and it doesn't seem like it's gonna end.

Also, they keep saying " Come back whenever you're ready, I'll always want more tech ", which I assume is a way of telling me its infinite.

So nothing 100% certain, but by the looks of it, there are infinite side quests at least in some cases !