Toward the end of the show the Captain is reunited with his now cured dog. The beagle jumps out of the cage onto his shoulder. This scene was filmed in 2 parts; the first one has the dog landing high on his shoulder, then a cut and the dog is jumping and landing considerably lower down.
If the species of chameleon that Dr. Phlox uses to give Porthos a pituitary-gland transplant is similar to those on Earth, as is implied, it would never have worked in the same manner as a dog's pituitary gland.
Phlox asks the captain to get a "5 cc'd" of a medication. The term "CC" (meaning cubic centimeters" is not used for liquid measures even in the 21st Cnetury. The request should have been for 5 ml (milliter).
Several shots of Porthos in his isolation box reveal him to be an obvious prop and not a real dog.
While Porthos is in the incubation chamber, on careful observation it's obvious he's not breathing.
Archer is angry with the Kreetassans because he thinks they did not bother to check and see if there were any pathogens in their environment that would be harmful to Porthos. However Dr. Phlox tells him the virus that is breaking down Porthos' immune system should not be affecting him the way it is, and that he does not understand why it is shutting down his immune system. So if Phlox cannot understand how or why the virus is affecting Porthos the way it is then it would be reasonable that the Kreetassans would not have been able to know or predict that the virus would be harmful either, especially considering the fact that they having nothing like a dog on their planet.
Pathogens typically evolve to target certain species and will only affect those species and others that are closely related. It is implied that Kreetassa does not have anything similar to dogs so it is unlikely that there would be a pathogen that could affect Porthos.
Dr. Phlox tells Captain Archer about Porthos' condition by saying that his autoimmune system had collapsed. While there are autoimmune conditions in which one's immune system attacks healthy tissue or cells, it would be more appropriate for Dr. Phlox to say that Porthos' immune system had collapsed.