That just looks like an ageing kettle to me. As part of the boil cutoff mechanism, some steam / condensation makes its way into the internals (and maybe a tiny amount of seepage). This is normally prevented from building up by a drip hole in the bottom, but the environment is very humid. Shaking and tilting probably causes some condensate to drain.
If the kettle isn't causing an earth leakage trip, then it isn't bridging the insulation gaps that are deliberately designed for the conditions. Carefully avoiding overfilling is about the only way of reducing moisture in the base.
If dripping becomes excessive, or operation fails (burnt out contacts or broken bimetal click spring), there is no real alternative to replacing it.