What are the limitations of using models in science?
George Box said in the 1970s "All models are wrong but some are useful." This points out a major limitation of models: models can never be a truly perfect representation of processes in the real world, that is, of natural processes as opposed to artificial/manmade processes.
Stemming directly from this major limitation is the problem that scientists can be overconfident in their models because they seem to work very well. Certainly a model that works effectively in practice and gets the job done is very useful. But overconfidence in a model can lead to bias; one might favor that model over newer models that might be an improvement on the existing one. No model can be absolutely perfect, but one model can be better than another by particular chosen measures (usually predictive power and simplicity). The tendency to hold on too tightly to models that are accepted in the community and work well when there are other candidates coming to the fore does slow down progress in science. For example, Einstein had a strong belief that the universe was in a steady state and so, even though his equations suggested that the universe is currently expanding outward from a starting point, he manipulated his equations to keep them in line with his underlying bias. He called it his "biggest blunder" as it delayed investigation into the possibility of an expanding universe by decades. But remember: the Big Bang Theory is just a model, too.
George Box also drew his reader's/listener's attention to the principal known as Occam's razor, which posits that the researcher "should seek an economical description of natural phenomena." Occam's razor (Occam was a 13th century Franciscan friar) is a name given by scientists to the principle of keeping things simple (you may have heard "keep it simple stupid" or KISS, which is a more modern name). The idea is to try to keep your model as simple as possible while still retaining the same accuracy in terms of prediction.
Though there are limitations to models in science, there is no alternative route. Science is all about models. When we observe phenomena we do, however, create models in our brains, which is useful for adapting our behavior to our surroundings and hence for survival. But this is purely internal, and not that well understood, even though it is going on literally under (or behind) our noses. To communicate science to others we need models. The thing is to remember that they aren't perfect (as even the models we create in our brains aren't, though they may be considerably more sophisticated and not necessarily obey Occam's razor!), and so not to put too much store by any one model, and to keep them simple wherever possible. Of course, it should be mentioned that more and more computers are behaving like our brains and juggling very complex information. But people still need to be behind those processes, and as the sci-fi genre keeps reminding us, we need to be careful the computers don't take over.