Recent operation of JET with centrally strongly reversed magnetic shear, produced with the help of lower hybrid current drive, has extended the domain in which internal transport barriers (ITBs) can be formed in JET. Performance is frequently limited by magnetohydrodynamic (MHD) instabilities in these reversed shear regimes. The most severe limit is a pressure driven kink mode which leads to a disruption. This disruptive limit is essentially the same in ITB plasmas with low or strongly reversed shear. Unique to the reversed shear regime is a dominantly n = 1 mode, which has multiple harmonics. This mode is a seemingly common limit to performance, in the highest performance plasmas. Also unique to the reversed shear regime are q > 1 sawteeth events, which can in turn trigger n = 1 post-cursor oscillations. In general, these post-cursor oscillations are benign but do provide valuable information on the q-profile. Other instabilities, including 'snakes' at the outer q = 3 surface, are also observed to limit the performance of reversed magnetic shear ITB regimes.