Magnetization reversal in exchange biased Co/CoO dot arrays has been investigated systematically as a function of shape anisotropy, dot size, temperature, cooling field and training effect. Polycrystalline 24 nm Co films have been sputtered on a pre-patterned Si/SiO2 substrate with the lateral dimensions of the dots varying from 200 to 900 nm at a fixed spacing of 800 nm. The Co dots have been oxidized using pure oxygen to create a Co/CoO bilayer. Below the Néel temperature, the hysteresis loop of this bilayer displays a normal unidirectional shift due to the exchange bias in the continuous film, while the patterned film displays an additional anomaly of the upper part of the hysteresis loop. This anomaly, which is shape dependent, increases with decreasing temperature and cooling field. On the other hand, it decreases for the trained loops with increasing aspect ratio (length/width) of the patterned dot. This anomaly is probably caused by incomplete biasing due to the competition between magnetostatic inter-dot interactions and exchange bias.