All heaters can be dangerous, especially if they are used incorrectly or not properly maintained. Surface temperatures can be high enough to burn skin if contact is sustained.
Oil-filled column heaters have lower surface temperatures than most other types, especially the styles with wide or shielded fins. All styles of column heater are tall and heavy and can cause injury if falling on a child, but again, the wide-finned versions are safer in this respect.
All new heaters have to pass stringent safety tests to ensure that fires don't occur if the heater overheats due to air inlets being covered or blankets or towels falling on the heater. But these safety standards were not in place when many of the older types of heater now available in second-hand shops were made.
A tilt switch is a good safety feature: it will turn the heater off if it tips over.