Dichloromethane cleaning
Safety regulations in every lab I have heard of strictly disallow mixing of containers of any sort that contain, have contained or will contain chemicals with containers of any sort that contain, have contained or will contain food, beverages or anything else intended for human consumption. You should never drink out of a bottle that had contained chemicals, you should never store food or drinks and chemicals together and you should not consume anything where there are chemicals. Your question has a premise that should never happen due to safety regulations.

With that gotten out of the way the answer is quick and dirty: It’s not the dichloromethane that is your prime point of concern. Dichloromethane boils at $40~\mathrm{^\circ C}$ and if you keep a bottle that contained it open and lying down overnight at room temperature, there are no traces of dichloromethane in harmful concentrations left. But unless you really go out of your way to buy $99.999~\%$ purity dichloromethane, it will contain impurities which generally do not evaporate as easily, i.e. which will stay in the bottle. Since no bottle of dichloromethane is designed for drinking out of it, there are no safety tests performed with these impurities or additives and thus you cannot assume it to be harmless even if dichloromethane is gone.

You should not read this answer to say that bottles of highest-purity dichloromethane be safe to drink out of. Never mix food or beverages and chemicals. Never, ever!