The Bohr model gave a picture of the hydrogen atom which was very successful, explaining all the lines in the spectrum then known, and predicting more which were found. It put on a semi theoretical basis the Rydberg formula, which until then had been a purely experimental formula.
The Bohr model was in extremely good agreement with experiment, and the value of the constant calculated is again in extremely good agreement with the Rydberg constant, with the advantage that a value for the Rydberg constant can now be calculated from known physical constants.
There were real limitations to the Bohr model however.
The Bohr model could only accurately be used to model the energy levels in the hydrogen atom. Attempts to extend it to explain the spectra of heavier atoms with more than one electron failed.
The postulate on which the Bohr model was constructed, that the angular momentum of the electron as it orbited the nucleus was quantized in integral multiples of
had no theoretical basis. It was not known why angular momentum should be quantized or whyshould be the unit.
It failed to explain why electrons should not continuously radiate energy and spiral into the nucleus. The electron in orbit is after all, being continuously accelerated. An accelerated charge should continuously radiate energy.
The Bohr model could not explain the relative intensity of the different lines or why the relative intensities at different temperatures should be different.
The lines of hydrogen exhibited fine structure, with each energy level actually consisting of several closely spaced energy levels. The Bohr model falied to predict or explain this.
Though a massive advance over previous models, which failed to explain or predict anything about energy levels in a theoretical manner, the Bohr model itself did not rest on theoretical foundations. Physics was waiting for a better theory.