Although it's a clear continuation, the story make a good effort to be accessible for new readers with the first page seeing a loose tongued ship's cook detailing the basics to set up the quest. But where the reader is likely to be deceived comes when Thompson and Thomson turn up at the ship Sirius to explain that Max Bird, one of the villains from the first part, has escaped custody. Later on they join the ship in order to provide protection, stating that Bird was seen near the vessel the night before it departed and they have been assigned to protect Tintin and Haddock. But whilst this provides an initial red herring in the mystery of who's been taking things aboard the ship, the thread is ultimately lost as Bird never appears. Indeed, given the usual efficiency of the Thom(p)sons, it's tempting to wonder if Bird ever actually escaped and the whole story was in fact an invention by their superiors trying to get rid of them for some weeks.
Indeed throughout this story there are lots of hints of conflict to come only it doesn't turn out that way. At the start the ship's cook is overheard in the pub by a sinister looking man - but he turns out to be a reporter who breaks the story. During the voyage, Captain Haddock assumes there's a bomb on the ship but in fact it's the parts for Calculus's submarine. On the island it seems as though Tintin and the others will have to face a tribe of cannibal natives but in fact they've long since disappeared, leaving just an idol and bones. Again and again this story seems to be setting something up in line with previous adventures, but each time it doesn't happen. Thus we have a story in which the biggest threats are sharks, drunkenness and stupidity.
More so than any previous story this is a straightforward tale of exploration with no antagonist to disrupt proceedings. So instead we have an extended portrayal of preparations for the expedition, the voyage across the ocean, the exploration of the island, the underwater excavation and the disappointing return home before the final discoveries. As a result of all this the story is one of the quickest of the Adventures to read (and it's one of only three that were told in a single episode in the 1990s cartoon) with one of the briefest plots.
Instead the emphasis is very much on the characters, with the last major member of the supporting cast introduced here. Professor Cuthbert Calculus is the latest in a long line of eccentric scientists and inventors, with a heavy degree of deafness that drives a great deal of the humour in his scenes. He proves utterly unable to take "No" for an answer and winds up stowing away aboard the ship together with his newest invention, the shark submarine which appears on the cover. Despite being presented as a scientist (made even more explicit in the original French where his surname "Tournesol" means not just "sunflower" but also "litmus") he is also a practitioner of dowsing, often believing his pendulum when the facts overwhelmingly point the other way (perhaps an error as the pendulum keeps pointing west when the more direct route is east). He proves a highly likeable character and literally proves his worth at the end when he reconstructs the documents found on the wreck of the Unicorn to discover that Marlinspike Hall is Haddock's ancestral estate, then provides the money to buy it back.
The introduction of Marlinspike adds to the confusion in translation about just where the series is based. In the English translation the hall and surrounding estate was given to Sir Francis Haddock by Charles II of England (and Scotland and Ireland), which would agree with the England address given in The Secret of the Unicorn. But this makes a nonsense of a key scene where the island appears to be completely missing from the co-ordinates given, until Tintin hypotheses that Sir Francis used a French chart based on the Paris Meridian, thus placing it further east. The exterior of the hall is now shown and it's all too clearly based on real life French châteaus, so it would have made more sense to stick to the original setting in Belgium. It's a sign of the problems of relocating characters in translation when it would have been easy for a sailor's descendants to be in a different country. (There is the objection to the original version that in real life France did not control Wallonia in the late 17th century, but there were a number of wars over the territory and it's conceivable that the manor was a spoil of war.)
The (re)acquisition of the hall leads to one of the biggest jokes in the entire Adventures - the whole expedition didn't need to happen and the treasure was back home all the time. It's true that the expedition brought Calculus into Tintin and Haddock's lives and he provides the money for the hall, which they learnt about from the documents on board the Unicorn, but it's reasonable that this could have all been discovered back in Belgium. Of course, this wouldn't have made for much of a story and so it would have been possible to tell the tale in a single album with Haddock reacquiring the hall by some other means.
This reflects the constant theme of red herrings throughout the story, with false expectations raised time and again only for the tale to take a different twist. The only great depths to the plot are the ones explored by Tintin and Haddock but this isn't aiming to be a great mystery or unsubtle political commentary. Instead we get a straightforward story of exploration with what were then some of the latest scientific gadgets to aid the quest. It may ultimately prove inconsequential but this is quite an enjoyable little adventure.