The suspects include the governor, the ex-governor, the chief of police, and a Buddhist abbot — until one of them is murdered. Meanwhile, Akitada and Tora have become involved with a pair of sisters, the daughters of a crippled martial arts teacher. The plot is adequate, but rarely rises above the cliches of the genre. Most of the events are signalled well in advance and there's never any real tension, either in the mystery or in the various threats to the principal characters.
The historical setting is used only superficially, for objects, customs, and so forth. It is fleshed out with bits of more recent Japanese culture and some "generic medieval" background, but it would only take changes to the names and a few individual words to relocate The Dragon Scroll to (say) the Roman Empire.
The characters think and act just like modern Americans. Akitada's relationship with Tora, for example, carries with it a modern attitude to class differences, while his relationships with women are driven by early twenty-first century sensibilities. Just compare The Dragon Scroll with — to pick an example from my recent reading — a novel such as An Instance of the Fingerpost. This is set in 17th century England, far closer to us than Heian Japan both culturally and temporally, but its characters are much less modern than Parker's. (On this inability to escape suburbia I recommend Ursula Le Guin's essay "From Elfland to Poughkeepsie", which is about fantasy writing but is largely applicable to historical fiction as well.)
The Dragon Scroll made decent escapist reading while I was down with a cold, but it was also rather frustrating. Heian Japan is such a fascinating milieu that I couldn't help wonder what a real historical novelist might do with it. We may not know that much about eleventh century Japan, but it sure wasn't anything like the world depicted here.