the watch came with box and papers and also a service-history (new full service in august 2017 costing 455€ (round about 500$) they renewed the crystal, crone(s), hand-set and last but not least "Barrel Bridge - Jewelled Rhodium-Plated".
So there is most certainly an issue. It appears at the last service they replaced the barrel bridge, and in the era this watch was made, the serial number was on the barrel bridge (it was later moved to the balance cock). When this bridge was replaced, they didn't take the step of getting the new bridge marked with the serial number, so now your movement has no serial number on it.
This is very unusual, because typically a proper service center would not do this sort of thing, but a new bridge with a serial number on it has to be ordered from Omega in Switzerland, and they would have to send the old bridge back for exchange, because obviously Omega doesn't want to have more than one part out there with the same serial number on it. So the first questions is, do you have the old bridge with the serial number on it? If not, it may be difficult to get the serial number reinstated on the movement.
Personally this is reason enough to return the watch, but if it for you that's another story.
The second thing is, although I don't have an exact cut off date when Omega moved the serial number from the barrel bridge to the balance cock, my guy feels that having the serial number starting with 80 million should have the serial number on the balance cock, so that brings up the question if this watch is a put together with a case that doesn't belong to the movement. For example, I just serviced a watch of the same exact model, and the serial number started with 8042, and it had the serial number on the balance bridge, so was made after the switch in location on the movement.
If I read the serial number on the paperwork correctly, it is 80456712, so made after the one I just serviced, yet the serial number is on the barrel bridge - this doesn't make sense to me.
I have confirmed that the serial number 89456712 is for a 25318000, but I question if this is the movement that was in this case originally.
If you have the old bridge and it has that number on it, this is a non-issue, but if you don't this is another red flag for me personally.
Cheers, Al