My advice.
Hi Tom,
The Seamaster name first appeared on an Omega in 1948.
Early models didn't have the "hipocampus" ( Seamonster ) on the back. I'm not sure when this first started appearing. So yes, it is perfectly normal for older Seamasters not to have the Hipcampus on them.
As with any sucessful product, there have been fakes made. ( as Georges said the Seamaster 300 from the 60's/70's has been faked a LOT )
eg. Ignore anything with "antimagnetic" on the dial or anything with the number of jewels written on the dial.
What you may find after 50 years, is that many genuine watches have been fitted with the wrong hands, bracelet etc etc
All I can suggest is that you take some time to research your watches. Feel free to post watches that interest you here. We can try to answer questions. I say "try" because it is difficult to find a specialist for "dress" Seamasters sometimes.
If you don't have a copy of the "japanese" Seamaster book, I recommend you find/get one. It is without doubt the best Book on Seamasters currently available. And, even though it is in japanese it is still packed with useful info ( dates, movements, case Refs & PICS !! )
This is what the front cover looks like
Good luck with your search.
Steve