We show that there is a subtle instability of the T' structure for the R2CuO4 (R = rare earth) compounds at the center of the R series with the boundary at R = Eu. Crystals grown in Pt crucibles and PbO flux show weak ferromagnetism (WF) and two temperature-dependent forbidden Raman peaks. Crystals grown in alumina crucibles and CuO flux do not show WF and the forbidden Raman peaks are much weaker. The WF and forbidden Raman peaks in Eu2CuO4 suggests that the instability of the T' structure is associated with O(1) displacement in the CuO2 planes.