Using density-functional theory with the on-site Coulomb correction (the local-density approximation plus U method), we perform the structural optimization of BiMnO3 by starting from different experimentally reported structures. We confirm that, irrespectively on the starting condition, all calculations converge to the same centrosymmetric structure, in agreement with the previous finding. Nevertheless, the structural optimization substantially reduces the Jahn-Teller (JT) distortion in the system. We attribute this fact to the strong competition of local distortions around the Mn and Bi sites: while the local Mn environment experiences the JT instability, the one of the Bi sites favors the off-centrosymmetric displacements, which involves the same oxygen atoms. The presence of the second mechanism explains the difference between BiMnO3 and more canonical JT manganites, such as LaMnO3. Finally, being motivated by experimental studies, we have investigated the formation of different types of defects and obtained that in BiMnO3 (contrary to the other considered systems, such as LaMnO3 and BiFeO3) one can relatively easy create the oxygen impurities at interstitial sites. The impurity oxygen atom tends to form a pair with the host oxygen, which explains the insulating character of the oxygen-excessive BiMnO3+x. Moreover, we found that the BiMnO3+x samples experience the "memory effect," where the optimized crystal structure strongly depends on the starting configuration. We suggest that such a memory effect may explain stability of some of the crystal structures of BiMnO3, which have been previously reported experimentally.