The author's excellent 'powers of observation' [=ability to notice and pay close attention to things] are evident in the book's detailed descriptions.
The plants seem to have recovered from the disease, but they are still 'under observation'. [=someone is watching them carefully]
They're keeping him at the hospital 'for observation' [=so that doctors can watch him carefully] for another few days.
(..) I may need one of those in a few hours. Consider it a wedding gift. Watson... Might we use an alternative exit? Is there something different about you? I'm under observation. As you should be. You drive. Will your beard, Be with us... All night? I'll remove it once we're south of Trafalgar Square. If you believe Moriarty has you under observation, Isn't this a bit conspicuous? It's so overt, It's covert. Trafalgar Square... Why are you looking at me with such concern? I'm so very worried... (..)2011 Sherlock Holmes: A Game of Shadows