They do it with mirrors is classic Christie. Miss Marple goes to stay at the home of an old friend, after old friend's sister has approached Miss Marple worried that there is something "wrong" about her sister. The sister, Carrie Louise Serrocold, certainly lives in an odd house; a sprawling Gothic monstrosity owned by her first husband, the fabulously wealthy and philanthropic Gulbrandsen. Her second husband, Lewis Serrocold, has turned the property into a home and training centre for juvenile delinquents, and there are some distinctly peculiar people (not least the psychiatrists) living in the property, but as far as a threat to Carrie Louise is concerned, Miss Marple is not at first aware of anything.
Then on one memorable evening a young delinquent, Edgar Lawson, attacks Serrocold, and, coincidentally, Carrie Louise's stepson is murdered. As the body count rises, Miss Marple is forced to look at the situation in a completely different light....
In many ways this is classic Christie, although set and written in the 1950's. The classic country house setting, a strong cast of characters, Christie's love of the theatrical, and a new twist on the traditional "locked room" mystery. The actual central murder is very cleverly done, and it's a fun read, even if the murderer is not wholly unexpected. Christie writes convincingly about the small nuances of daily life that can make themselves felt, even if they're not wholly explicable. What I mean by this is the traditional psychic "I knew something was about to happen to X" - well, yes, you knew, but not by any supernatural means - you knew because he suddenly started to act oddly - nothing major, just tiny changes that barely registered but were apparent at a subliminal level to those who knew him.
Where the novel falls down is when Christie attempts to examine youth culture. This became an increasing obsession in many of her later novels :The Pale Horse, Hickory Dickory Dock for instance. She never writes terribly convincingly about this, and it can often read as rather hysterical. Not one of her best, but a fun light read.