The Super Mario Bros. Super Show! episode Bats in the Basement
September 13, 1989
The eighth live-action segment of The Super Mario Bros. Super Show! is about a vampire called Count Zoltan Dracula visiting "Mario Brothers Plumbing" as part of an excange program, and while noticing how he spends the whole day sleeping in a coffin, Luigi mentions that Mario normally sleeps all day too, unless there's an Inspector Gadget marathon on TV.
The Super Mario Bros. Super Show! episode Defective Gadgetry
October 27, 1989
the fortieth live-action segment of The Super Mario Bros. Super Show! is about the Inspector Gadget visiting "Mario Brothers Plumbing" to have his gadgets fixed. After totally disassebling him, they then put him back together, only with some modifications, causing even more trouble to the inspector.
The Inspector Gadget's appearance is quite accurate to his look in the cartoon, and he's played by Maurice LaMarche, who voiced Cheif Quimby in the Inspector Gadget cartoon, but later voiced Gadget himself starting with Inspector Gadget: Gadget's Greatest Gadgets and in every subsequent animated movie and in Gadget and the Gadgetinis, making this the most accurate live-action incarnation of Inspector Gadget.
The fact that he gets disassembled, however, is something unusual to the cartoon, where he mostly acts as a regular policemen with gadgets built in his coat and hat, and while he's implied to be cybernetically enhanced, he's never confiremd to be a cyborg.
A minor note goes to the gadgets used in the episode, that probably due to the adaptation for live-action, look differently than they do in the cartoon, with the only exception of the Gadget phone. First, when Gadget tries to shake Mario's hand, he instead has a mallet coming out of his sleeve, but his Gadget Mallet actually came out of the hat in the cartoon, and he had no gadgets coming out of his sleeves. To sign the check for the Mario Bros. Gadget takes a giant pen out of his sleeve, put his gadget pen was actually in his left middle finger in the cartoon. Later, his arms accidentally extend in two springs, but he actually had telescopic tubes in the cartoon, while he only had springs in his legs. In the end of the episode he uses his Gadget rocket shoes, but in the cartoon he only used them in conjustion with his Gadget Skates.
About the two shows continuity, apart from the aforementioned differences, it's assumed that Gadget's adventures are canonical to this episode, since he receives a call from "the Cheif" , supposedly being Cheif Quimby, and later mentions Dr. Claw, howeve it's unlikely that this episode would be considered canonical to Inspector Gadget's series. It should also be noted that Mario and Luigi don't seem to recognise the Inspector, so it's assumed Luigi's sentence in "Bats in the Basement" to be ignored in this episode.
The Super Mario Bros. Super Show! episode Treasure of the Sierra Brooklyn
November 10, 1989
The fiftieth live-action segment of The Super Mario Bros. Super Show! is about the Mario Brothers searching for a buried treasure. To do so they call Inspector Gadget for help, and he promplty shows up.
The Super Mario Bros. Super Show! was created by Inspector Gadget's copyright holder DiC under Nintendo's license. They basically just included their original character in another of their TV shows.