Quilby says the invisibility formula works by absorbing light. This would not result in invisibility, but would instead make the person completely black.
No mention of the discrepancy between the $100K the couple paid for the formula and the $250K they withdrew from the embassy account.
At the end, in the house, the invisibility is explained by electronics moving the furniture etc and creating the voices. However that doesn't explain the invisibility events in the government offices in the beginning of the episode.
The final explanation for invisibility doesn't account for how the Russian got past Mrs. Peel at her apartment unseen, with his clothes visible immediately after.