If you are allergic to cigarette smoke or simply don't want to be exposed to it, make sure your written tenancy agreement states that you are in a non-smoking building. If the landlord breaks your agreement by allowing a smoker to move in next door when you had an agreement that it was a non-smoking building, you may be able to claim for compensation from the landlord. You will need to apply for dispute resolution through the Residential Tenancy Branch. However, if your written agreement does not state that the building is a non-smoking building, it may be you who has to pay if you are breaking a lease or moving out without proper notice.
For information on second-hand smoke, including its effects in multi-unit dwellings, please see the following:
Read about an interesting case regarding the smoking of marijuana in rental housing: