Thyroid follicular neoplasms commonly have aneuploidy, presumably due to chromosomal instability. This property is associated with a greater malignant potential and worse prognosis. Recently, there has been considerable progress in our understanding of mechanisms that may account for chromosomal instability in cancer cells. Many tumors with chromosomal instability have abnormalities in the cell cycle checkpoint that monitors the fidelity of mitosis. Mutations of Bub1 or BubR1, genes coding for kinases involved in mitotic spindle assembly checkpoint signaling, are found in a small subset of aneuploid tumors. Other components of protein complexes responsible for attachment of kinetochores to microtubules, or for cohesion between sister chromatids, may also be subject to alterations during tumor progression. Here, we also discuss the evidence that certain oncogenic events, such as Ras mutations, may predispose cells to chromosomal instability by favoring inappropriate posttranslational changes in mitotic checkpoint components through activation of upstream kinases during tumor initiation or progression.