I would love to know if that description is accurate to your experience with the books. Not whether you found it bad or good necessarily, just whether or not it rings true.
For me it does tend to make the books an up and down affair. If the chapter you happen to be on isn't doing it for you it can drag. On the bright side you also know that the next chapter will likely be about something entirely different.
Does the third one involve them escaping into Spain? Or the second? They seemed to trudge rather than escape. I'd agree with staying immersed in the overall story because that would be the strength of the series; building to much more than the sum of its parts. Sometimes it felt like plot threads were going to get picked up later; the love interest, for instance. This would be a realistic treatment (sailor goes off to sea) rather than a dramatic one, but if your mind wanders (mine must have) you might feel lost jumping back in. However, you are right that each story was still self-contained enough to be enjoyable. It feels like the rewards would really kick in as the series gets into the later books. I wish I could read with that level of commitment. Blimey, isn't Master and Commander (the film's basis) book 13 or something?!
The second book has them sneaking out of spain (trudging is the right word for it), the third one has Stephen captured at Minorca.
I have been surprised by a few things that have popped back up in the series that I thought were somewhat trivial at the time. Ships, names, etc. I hope that happens more and more as I continue.
Master & Commander is book 1
But even as far as book 3 I was recognizing moments that I thought were part of the film. The film kind of feels like a "best of". I expect I'll continue to come across nifty bits that were included.