A problem for space contruction I can see for capital ships is the actual size of the plant, or dry dock. You can get automated systems to operate on the ship, but the main bottleneck is applying the refined materials to the ship itself, I currently don't see the full automated system working since I am assuming this is the current workload for the dry dock.
Construct the chassis/superstructure of the ship.
Apply internal 'deck' structure
Install reactor, engine, and basic sensor systems for diagnostics
Begin applying external armour units
Install life support modules, gravity module, weapons power units
Finish armour
Full installation of electronics systems
Install basic weaponry
Commence testing of vessel on a semi-operational level
Finalize installation of all optronics, weapons and sensor units
Test again for any malfunctions, and continue diagnostics.
Apply final external 'decals'.
Finish weapon testing, load up supplies.
Commission the ship.
A lot of the above is at the moment automated, except for the internal systems I believe, you can get robotic units to do it, but eventually, you need actual engineers on hand.
The only way I can see it being fully automated is if we build 'complete-dry-docks' where the entire internal superstructure of the shipyard can construct the ship without moving it at all. Meaning you can install 'slices' of the ship one at a time. In theory, it'll be faster, if each slice or piece is installed correctly. The main problem is the engines, reactor and optronic systems. They still need manual work.