It can depend on the elquid, but in most cases you will get a little cross over in flavour. If the last eliquid was very strong then it may well taint the new flavour. One trick I use is to use menthol eliquid as a wick cleaner. Just fill the carto with menthol ejuice and vape away then fill with the new ejuice you want to use.
Mind you with cartos being so cheap, it may be best just to use a new cartomiser every time.