Spot painting would be the best, make sure it's the same shade, lots of times they use a off-white.

Small spots you can elininate with an eraser.

If not very dirty you can also clean small areas with a damp rag, water and soap.

if you lived in the place you are about to vacate for more than twelve nmonths and walls are either wall-paper covered or with kind of plastered it is very likely original shades faded.  A white eraser ( the kind used in art classes) should do on some stains. In presence of dirt or traces of you might try lukewarm water on a sponge and dab on places if the support is not paper made.

However be extremely careful with touch-up paint if you do not buy/find the exact hue...Otherwise you will find yourself in a situation you MUST paint the whole wall surface on one side....if you do not want the owner to charge you for it.

Usually (99% of case) the owner or representative does not accept "patchwork" paint.

Good luck

I covered some stains after 2 1/2 years with the same painting... it blended in perfectly.

@Catalin: you were a smart tenant from the moment you moved-in since you painted the walls first and then had kept leftover paint for the days you'll move out or used same referenced colour from same store. That may explain some. Depending on paint manufacturer and/or origin the off-white (in this instance) has many different hues. The story be the same if we would be considering shade of pastel pink or pastel yellow. It is fair to issue words of caution.

Hi Jane,

The exact colour for white room's plaster wall in Switzerland is "RAL 9010". You can find small pot at market like "Jumbo" or "Obi" or "Coop" ... Ask the seller specialized for it first.

Cover marks/stains with small perpendicular touches with paintbrush. For larger stains, better with roller...

For smaller stains "Tip-Ex" has also same colour.