Congratulations on buying a watch you like
@Emiliodk - and welcome to the forum.
I hope you understand that members here are just trying to look out for your best interests- not because anyone knows you, but because there are so many shady dealers out there that give the hobby a bad reputation and the goal is to educate anyone who comes here looking for advise.
A couple points that I think are very important (albeit moot now that you have already purchased it) :
Did the seller provide you with the serial number on the movement (not the reference number on the case)? Sometimes a seller will guess at the year the watch was produced and not actually verify the serial number or order an extract of archives from Omega which will tell you exactly when and where it was delivered originally. Even without an extract, you can get close with just the serial. Normally most don't really care, but since you specifically bought this as a birth-year watch, I would ask the seller how he verified the year of production.
Secondly -what is this dealer's idea of a "full service". So often watches are listed for sale as "serviced", but all the seller did (if they even have any experience working on watches) was oil the balance and reset the timing to get it closer to accurate. Sure it will be running when you get it, and may even run well for years, but that doesn't mean it was properly serviced (full strip-down, cleaning, replacement of worn parts, replacement of crown and seals, oiling, retiming etc) and continuing to run the watch on dried up oils and worn parts will end up causing more problems down the line.
If the seller is using a watchmaker for service, then he should be able to provide you with an invoice for the service which details the parts that were replaced, the verification of a pressure test, and the stats for the running condition of the watch. If the seller said he "serviced it himself", then I would be very skeptical of the service unless he is a trained watchmaker, and if so- I would want to read reviews or get referrals for his service work, not just sales referrals. If he said notparts were replaced, then he didn't do a service. At the minimum the mainspring, crown and gaskets should all have been done.
Genuine factory Omega parts are now limited to only watchmakers with parts accounts, so if the watchmaker used to service this watch (or the seller himself if he said he serviced it) does not have a parts account, it is questionable wether the service was done to factory spec.
Again, congrats on the watch-it looks lovely
