When Frasier (Kelsey Grammer) first asked Niles (David Hyde Pierce) to join Frasier and Martin (John Mahoney) on their trip, Niles refused telling Frasier that as his brother, Frasier is entitled to bone marrow and one kidney, but not a Winnebago trip. However, in season two's Someone to Watch Over Me (1995), Frasier's bodyguard (Alyson Reed) tells him she needs a list of family members who are willing to donate organs should anything happen to him at the awards ceremony. Niles then tells Frasier he has abnormally small kidneys, indicating he would not be willing to give one to Frasier.
They are afraid to re-enter the US from Canada without passports, but they were able to get OUT of the US. Response: There was no issue with passports. Daphne explained that she was not allowed to leave the United States until she had her green card.
The shots from exterior of the 'Winnebago' reveal it to be a studio mock-up. For example the parked windshield wipers make no contact with the windshield.
During the beginning of the road trip as Frasier (Kelsey Grammer) is driving, Martin (John Mahoney) instructs him to get over a lane for the upcoming exit. However, if you watch the back window you can see they are on a one-lane road.
In the final scene, Martin mentions that they're 2 hours from Seattle, on a road that leads directly into it. A minute later, Frasier looks at a map and says they're not far from Yellowstone National Park. This is a geographic impossibility; it takes about 12 hours to drive from Seattle to Yellowstone, so no way were they "near" it at the same time they were 2 hours out from Seattle.
When the boys see the sign for 'photos with a live bear', they remark the sign said 1 mile. In Canada at that time, distance was measured in kilometers.