The nature of a model is that it accurately represents only a portion of the modeled object; for example, model trains accurately represent the shape and proportions of full-sized railroad equipment, but they do not reflect their material components, physical weathering, smell, sound, and so forth. This shouldn't be seen as a problem with models; instead it should be expected and exploited so that a model does an excellent job of representing the thing that it chooses to focus upon and allows another model to do the same for other aspects of the modeled object.
Many of the models used in organic chemistry strike a balance between representing the physical dimensions of a molecule, representing its behavior, and being easy to understand. For example, the Bohr model is still frequently used in diagrams, despite having been known to be an inaccurate representation even in Bohr's time; however, it's one of the easiest ways to depict protons and electrons when focusing on atomic identities. It avoids having to include the complexities of quantum models and rendering the subject nearly impossible to draw.
When we use these models, one of the most important things we should assume is that the model is incomplete; there will inevitably be some aspect of the model that fails to fully capture our full understanding of organic chemistry. Likewise, we can assume that each model has certain circumstances or problems in which it is best, or, poorly, suited for the task and that we need to have a full understanding of the problem, not just the model, in order to choose the best representation.
Finally, we can assume that, since models are developed by humans, and those humans may make mistakes, have personal agendas, or have different professional opinions, it's possible that a model may not be fully accepted by certain members of the relevant community and that the choice to use or not use this model may have implications beyond that of chemistry itself. For example, the Ligand Field Theory is a currently disputed model, and the Copenhagen Interpretation of Schrodinger's Equation was disputed by Schrodinger himself, leading to the famous "Schrodinger's Cat" analogy, which was actually intended as a criticism rather than a representation of quantum states.