When the reporter announces that Baragon is attacking Paris, it is actually Gorosaurus. The Baragon suit was loaned out to Tsubaraya Productions for use on one of their television series and wasn't returned in time for filming.
Even though about 40 years have passed since the previous movie, Godzilla's son Minilla still looks exactly the same as before and he still has trouble breathing atomic rays. While one can argue that maybe monsters age slower, in his debut film Minilla grew from a infant into a much larger child under a very short time.
The Kilaaks exist in a temperature of at least 7,000 degrees. But several humans captured by the Kilaaks from Monsterland are in both Kilaak bases on Earth and the Moon. They should have been incinerated.
It is evident that the monsters are small puppets in shots that show them from afar, since they barely move and some look a tad different from the suits used in the rest of the shots. In the movie's second-to-last shot in particular, the Minilla puppet is stuck with its mouth agape.