Ive used no more nails to glue a mirror to a wall when i couldnt be bothered lining up the screws right and it hasnt fallen yet so must be good. But as its quite important that it doesnt fall off might be better using a specialist glue for plastics like this one.
http://www.maplin.co.uk/module.aspx?...013&doy=search
probably a bit cheaper too as you only need a little bit