I'm assuming that you're referring to a physical model of a DNA molecule.
One limitation of this representation is the fact that it comes nowhere near representing the actual size and complexity of a gene, let alone an entire genome. This is a fairly common issue with models of very large or very small things; the scales involved are very difficult for most people to visualize and understand, because they're beyond anything that we are accustomed to working with. Similar to the way that it's hard to visualize the many trillions of miles between the solar system and Proxima Centauri, the nearest star, it's difficult to visualize the size of a genome and the approximately 3 billion base pairs in the human one. A model helps with understanding what is taking place on a site-to-site, base-to-base level, but even a single gene is usually several hundred base pairs long.
Another limitation is a representation of the actual shapes and sizes of the atoms in DNA, as well as the different types of bonds involved. For example, the hydrogen bonds that give DNA its helical shape, as well as bonding the base pairs to each other, are often omitted, or represented in the same way that ionic and covalent bonds are, which might lead an astute observer to wonder why the base pair bonds can be broken and reformed, but not any of the others.
Physical models also tend to lack the flexibility and motility necessary to represent the functions that DNA performs; for example, the act of transcription would be very difficult to represent succinctly with a model.
One significant draw back of DNA models is that they don't effectively demonstrate the epigenome. The epigenome is made up of chemical compounds that help determine how the genes will be have. This plays a huge role in gene expression. Say, for instance, that a person has the genetic marker for diabetes, but they take excellent care of themselves and get plenty of excersize. The chemical compounds that make up the epigenome of that gene could suppress the expression of diabetes. Conversely, if the epigenome is negatively effected by diet and excersize diabetes could be actively expressed. DNA models do not sufficiently demonstrate the complexity of gene expression.