Your landlord is not legally entitled to put a camera inside your apartment (or to make a pinhole camera in one of your walls or to bug your apartment). If you suspect that your house is bugged or rigged with cameras, contact a security specialist who can inspect your apartment. If anything comes up, you'll need to directly consult with a lawyer on what to do.
However, if your walls are thin and he owns adjoining units housing gossipy neighbors, or if he occupies one of the units himself, he's not obligated to plug his ears to what people say or what he hears himself.
It would be an extreme violation of your privacy for a landlord to use a camera to monitor the inside of your premises. It is probably a violation of your right to quiet possession of the premises. It may even be a crime.
I agree with the previous answer: Contact a security or counter-surveillance expert and, if you find something, contact the police and an attorney immediately.
This answer is for general purposes only and does not establish an attorney-client relationship. An attorney-client relationship will not be established with me unless and until you have executed a written agreement for me to represent you. Kent M. Miller is admitted to practice in all state and federal courts in Connecticut. Any information provided outside of the State of Connecticut is provided as guidance only and not legal advice. You should use this guidance to assist you in your consultations with attorneys admitted to practice in your state.
Not only do I agree with the prior comments, but if you can't find the cameras, you might enlist a friend and stage a conversation that would draw your landlord out. Then if he bites, you would have your proof. But you need a lawyer to make sure to touch all the necessary bases.