When Godzilla is fighting Ghidorah next to the mountain, it is a stock shot from Ghidorah, the Three-Headed Monster. As Ghidorah knocks Godzilla into the bridge, the Mothra larva appears at Godzilla's feet, even though Mothra isn't in the film.
After the Godzilla Tower is destroyed, the shot of Godzilla
rising is from Invasion of Astro-Monster. When he gets up, Rodan is visible in the background, even though he never appears in the film, aside from a stock-footage shot used earlier in the film.
The balloon used by the heroes to lift up the wire to the top of the tower has a slightly pointy tip because it's not inflated entirely, but when it cuts to the miniature model, the balloon is almost perfectly round.
It is painfully obvious that in the shots which show Gidorah and Gigan flying, they are stiff dummies. In scenes that take place on the ground, both move around quite a lot, and Gidorah is always seen swinging his three heads about, so the flying scenes stand out like a sore thumb.
The main human characters, when they descend to the ground on a cable, it is obvious that they are mere miniatures in reality. For one, they don't have the proportions of a human being, nor do their clothes look like the ones the actual humans were wearing.
When Gigan crawls behind some trees, it cuts to stock footage taken from the film The War of the Gargantuas, and you can clearly see that instead of Gigan, it shows one of the Gargantuas from that movie hiding behind the trees.
The goof item below may give away important plot points.
When the alien bad guys die among the flames, the footage of the fire composited into the scene always remains in the same place in spite of the changing shots and camera angles. This also means that in some of the shots, the fire is clearly "rising" downwards.