The delegates discuss the tardiness of the delegate from Earth, and dismiss it because Earth is "many light-years away". However, Alpha Centauri is only a little over 4 light-years from Earth, and wherever Peladon is, the difference in distance would be a small percentage of the total distance, and the Alpha Centauri delegate is present. Even more, Mars is in the same planetary system as Earth, and the Martian delegates (the Ice Warriors) are also present.
When the TARDIS is wobbling on the precipice of the clifftop and about to fall off, the joins between some of the lower pieces of wood at the base can be seen moving.
No explanation is given as to how the Doctor manages to get the TARDIS working in order to travel to Peladon. The Time Lords had exiled the Doctor to Earth and blocked his knowledge of how to operate the TARDIS to keep him there.