It has been suggested that principal component analysis can identify slow modes in proteins and, thereby, facilitate the study of long time dynamics. However, sampling errors due to finite simulation times preclude the identification of slow modes that can be used for this purpose. This is demonstrated numerically with the aid of simulations of the protein G-actin and analytically with the aid of a model which is exactly recoverable by principal component analysis. Although principal component analysis usually demonstrates that a set of a small number of modes captures the majority of the fluctuations, the set depends on the particular sampling time window and its width.