Working at home has the advantages of being cheap and easy, with no wasted travelling etc, but there are all sorts of disadvantages to consider. As Amy said, if you have a look here, you'll find several discussions about it.
What would happen if the neighbours realised varies. If the place is yours, 'all' you really need to worry about is gossip. If you rent, then there will very probably be a 'immoral' clause in the lease and you risk having to find somewhere else to live.
If you do work from home, you want a cover story and to be prepared to move if necessary.