  In light of recent experimental results, we revisit the dispersive analysis
of the $\omega \to 3\pi$ decay amplitude and of the $\omega\pi^0$ transition
form factor. Within the framework of the Khuri-Treiman equations, we show that
the $\omega \to 3\pi$ Dalitz-plot parameters obtained with a once-subtracted
amplitude are in agreement with the latest experimental determination by
BESIII. Furthermore, we show that at low energies the $\omega\pi^0$ transition
form factor obtained from our determination of the $\omega \to 3\pi$ amplitude
is consistent with the data from MAMI and NA60 experiments.
