Is it dangerous to leave a bedside lamp on all night?

Firstly, it depends on the bulb. Low voltage LEDs are now quite popular in bedside lamps (particularly children's). These never get hot and so are far safer than the normal light bulb which can get quite hot after a while.

Secondly, it would depend on the wiring of the lamp. If it is old and has been moved around, there is always a chance of the wiring breaking or becoming faulty, therefore becoming a fire risk. This is why companies insist on wiring getting PAT tested every year. However, a new lamp should have been checked and is deemed safe in the first year. Obviously, there is always a slight risk with any wiring.