The paper analyses several examples of tacit influences exerted by mental models on the interpretation of various mathematical concepts in the domain of actual infinity. The influences of the respective tacit models, being generally uncontrolled consciously, may lead to erroneous interpretations, to contradictions and paradoxes. The paper deals especially with the unconscious effect of the figural-pictorial models of statements related to the infinite sets of geometrical points (on a segment, a square, or a cube) related to the concepts of function and derivative and to the spatial interpretation of time and motion in Zeno's paradoxes.