Conducting Atomic-Force Microscopy (C-AFM) has a strong potential for the characterization of thin silicon oxides on the nanometer scale. Here we consider difficulties and possible errors that may arise during C-AFM experiments. Using electrostatic simulations it is shown that very sharp tips can cause an inhomogeneous electric field distribution leading to an error in the measured Fowler-Nordheim (FN) current. Further, it is found that a water film, which is ever present under ambient conditions, on the one hand homogenizes the electric field distribution but on the other hand decreases the resolution of the measurements. For increased oxide thickness this water film leads to a ring formation in the electric field maximum and therefore makes an interpretation of FN current maps difficult. The occurrence of protrusions after the applying of voltage pulses and voltage ramps to the sample is investigated by comparing experiments under ambient conditions with measurements in ultra high vacuum (UHV). From this comparison we can conclude that the observed protrusions are real topographic effects, when a water film is present on the surface. However, for UHV experiments on a baked sample it is not yet clear if the protrusions are due to charging effects or due to a reaction with a residual amount of water.