Truthfully, nobody should be able to complain about the smoke coming from your BBQ. If it crosses standards for a hazard or an unreasonable nuisance, they'll have legal grounds to sue you. Neighbors can complain about BBQ smoke if it is a nuisance to them. The smoke can be a nuisance when it is widespread over the area and when the smell is too strong. If you BBQ just once a week and they have to smell it for an hour, too bad. However if you BBQ several times a week or if there is lingering smoke for a long period of time and it drifts into their house- not so good. You have a right to grill your food. However, you don't have the right to force smoke from your grill onto someone else's property, so they can take you to small claims court with pictures and evidence of smoke damage.