A major limitation of Rutherford's model was its inability to explain:
The stability of the atom and the atomic spectrum
Rutherford's model placed electrons revolving around a tiny, dense nucleus. According to classical electromagnetic theory, a charged particle moving in a circular orbit is accelerating and must continuously radiate energy.
The electron would therefore lose energy and spiral into the nucleus, so the model could not explain why atoms are stable. It also predicted a continuous spectrum, so it could not explain the discrete line spectrum of atoms (for example, hydrogen).
Isotopes were not what the model was built to address, the deflection of alpha particles was exactly what it did explain, and it had already rejected the idea of indivisible atoms.
Hence, the answer is: The stability of the atom and the atomic spectrum.
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