just wondering if the mistake on the hydra symbol is on purpose or accidental because if you look up the mythology the symbol they use is better suited to represent the kraken not the hydra as the hydra is supposed to be a giant serpent like creature with multiple heads the symbol used here is an form of octopus which is what the kraken is.
Ever since HYDRA was first introduced, the symbol has always been a skull with six tentacles. I don't think it was ever explained why they went with this design but I guess it could be that the skull can stand for death and destruction and the tentacles can stand for they way the organization can reach into the murky depths of the criminal world.
I know that's how the octopus symbol for S.P.C.T.R.E. from the James Bond films was explained. And it possible they based the HYDRA Logo off of the S.P.E.C.T.R.E. logo since James Bond was kind of an influence for Nick Fury and S.H.I.E.L.D. Of course it can all be easily explained as since they made Red Skull the leader of HYDRA, the skull stands for him.
I did add information about the creation of the HYDRA logo for the film on the HYDRA page in the Behind the Scenes Section if that helps any.
Well, I always interpreted it so that (in the movies, didn't read the comics) the skull is the Totenkopf (which is just German for "skull") skull of the real-world Schutzstaffel (SS, Nazi party elite guard/military arm), which Hydra began as a division of. That Schmidt became an actual "Red Skull" seems to me a case of "became on the outside what he already was on the inside" (i.e., Devil personified/the Nazi evil personified, ironically of course that's what he got when he wanted to become the Nazi ideal of "ubermensch" (literally, superman or superhuman)). It's quite symbolic, the evil being seen through the lofty bullcrap rhetoric.
As for the tentacles, for one, an octopus is not PR's favourite animal (despite real octopi being quite fascinating creatures, actually), as more often than not it carries negative connotations (kraken, generic sea monster, ugly, squishy, gross, weird, unnatural, etc.). Also, tentacles are fairly often associated with the quality of being far-reaching in influence, usually with a sinister and clandestine overtone (e.g. a nefarious organization, corruption in business or politics, behind-the-scenes control, etc.). Both of these fit Hydra well. Finally, the many tentacles may symbolize (modern) Hydra's many "heads", a compartmental structure, always some backup somewhere, omnipresence (as in the Shield infiltration, they really were in almost every team or department), etc.
So, overall, the symbol for Hydra both recalls its origins and founding philosophy ("new world order", which always remained from the Nazi era, even if they did abandon the narrow definition of Nazism even before the end of WWII), symbolized by the skull (which also, by an in-universe coincidence, evokes its founder), as well as its modus operandi (see above), symbolized by the tentacles. It's true the symbol doesn't have that much to do with an actual hydra (although the multiple tentacles still work for symbolizing the "heads"), but I think it's a very effective, well thought-out symbol on the part of the writers.
The S.H.I.E.L.D. symbol lends itself to similar analysis (which I won't bore you with here, unless you ask).
The poster features an octopus, however, the movie's special effects featured a hexopus or "sixopus" as they called it. Stan Lee and Jack Kirby (the penciler of Strange Tales 135) were known for "adopting" what was popular which in that era was creature features. Strange Tales has many of these creatures. More on that here: https://comiclists.wordpress.com/tag/jack-kirby/
The Reason they have a Octopus is because it is a great hunter and it adapts this was suppose to represent that hydra could adapt as well the reason their name is Hydra is because the term"Cut off one head and two more grow back" represents that if they kill one leader there will be more