..... I've deliberately stayed away from this question (right- or left-handed), waiting for others to respond. It is a tough one.
The male 'Octopus' (sensu lato, as in loosest sense - that basically means any-old octopus with 8 arms, no fins, 2 rows of suckers ....., excluding all of those pelagic and finned octopus families) USUALLY has the third right arm hectocotylised (for spermatophore transfer), although a very few species have the third left arm hectocotylised. So, there probably is some favoring of one side of the body to another when it comes to performing certain functions. Whether this is right- or left-handed I wouldn't want to say. The arms also perform many other tasks, so even the hectocotylised one is beset with myriad suckers and looks pretty much like a normal arm (although is often shorter and possesses fewer suckers, in addition to having a pronounced [at times] web extending out to the arm tip [the spermatophoral groove]).
The paper nautilus, Argonauta nodosa, usually has the third left arm hectocotylised, although I have a few male's here on which the third right arm has been modified into a hectocotylus (enclosed within a pouch). Whether these are mutations or not, again I wouldn't want to hazard a guess. Perhaps it doesn't matter which arm 'does the business'.
On quite a number of specimens of one Benthoctopus species in New Zealand, one of the arm tips (one in particular) branches at the tip. Now this is a rather rare thing (arm branching), and certainly to find this same bizarre condition in a number of specimens of one particularly rare deep-sea species is VERY odd! Whether the branch was driven by recurring mutation or damage I simply don't know, but if it is damage-induced then there certainly has to be some right/left handedness of the animal (as a species rather than individual), with certain arms performing certain functions.
Another thing to consider is whether it is as much 'right & left handed' as 'front and back armed'. There is often a marked difference in sucker size, presence/absence of especially enlarged suckers on some arms, and relative arm length to indicate that certain arms perform certain 'functions'; on a right/left axis there might be symmetrical performance.
It is the kind-of question that you could answer and say 'no, absolutely no right/left handed' business, but that's the kind-of answer that could land you in hot water when speaking to someone who has done extensive behavioural or neurological work on these brutes. I have done neither so will reserve judgement .... it would make for a very interesting research project.
... and yup, the brain is like an 'O', with the oesophagus passing straight through it (a donut we call it).
Cheers
O