When Fry and the professor travelled to Vinci (Leonardo's homeworld) in Leonardo's spacecraft, it took a month for them to reach the planet. After Fry stops Leonardo from killing his fellow inhabitants, he and the professor fly back to Earth in the same spacecraft. Farnsworth tells Fry that he's proud of what he did today. Moments later it showed them arriving at Earth, meaning it took them less than 24 hours to travel between planets prior to their month-long journey to Vinci.
Hermes' skeleton appears to have diminished in size by about 40% between the time Hubert re-fleshed it in "Rebirth" and when he was exposed to the x-ray intended for "The Last Supper," causing him to exclaim "Wait a minute, I'm not big-boned, I'm just fat!"
When Fry and the professor were travelling in Leonardo's spacecraft, it took them a month. That's a month without food, water, personal hygene items, and limited oxygen. They wouldn't have survived unless they had a secret compartment in the spacecraft.
When Leonardo activates the Macchina Magnifica, the blade cuts Fry's hair, but in the very next shot Fry is seen again, with his hair back in place, as if it was untouched.