Last week, I had engineered floor installed (floating - clicklock); today the contractors came to install the baseboard, and I noticed that a board next to the wall had been nailed down (on the long side). I checked and that appears to be the only spot in the room, so it was likely done accidentally.

I understand that you should never nail or glue down a floating floor. Is one board being nailed down something I should worry over? The nails they use for baseboard are 1 and half inch long.

Any help is appreciated!

Yeah, thats a potential problem. I'd ask them to come back and replace before it causes issues. Should be a breeze to fix.