This film isn't the atrocity the majority makes it out to be. When approached about it, yeah, most will criticize it for deviating from the (almost nonexistent) story of the original game.
As a kid, despite catching the tremendous differences from the games, I enjoyed watching it, and still do. It isn't a replication of the games, yet it's still entertaining and makes for a good laugh when contrasting between itself and them; comparable to the old animated Mario Bros. series. Both the movie and cartoons are very different from the games for which they were based, but those differences are what make them entertaining.
But I digress... If you're looking for a near-perfect film adaptation of the first Mario game, there is one. Produced in the year following SMB's release, "SMB: The Great Mission to Rescue Princess Peach," was an obscure anime movie that did a great job at capturing the essence of the Bros. initial Mushroom Kingdom adventure. Of course, anything is possible through animation. One could not say the same about live action in 1993.