Critical stability issues involving magnetic reconnection that are likely to influence the successful operation of burning plasma experiments are addressed. In particular, we discuss: (1) the stabilization of drift-tearing modes in weakly collisional regimes, with particular reference to nonlinear stability, including neo-classical effects; (2) the present understanding of sawtooth oscillations, in particular the interpretation of peculiar sawtooth features in FTU experiments with pellet injection; (3) reconnection near the X-points of magnetic separatrices.