I beat Normal Mode and Hard Mode once, but I played the Super Mario All-Stars version which saves after you beat each world, and I had to do the infinite lives trick in World 3-1. But I didn't use any Warp Zones.
Once, and you can bet your boots I used the Continue cheat (or should I say, the feature they didn't tell you about so they could sell you strategy guides). No Warp Zones though. Also, it was on an actual NES (SMB/Duck Hunt cart of course).
The version I beat wasn't official, it was the one where you could select between different game franchise protagonists.
I kind of assumed that as Mario, it was just like the original but there were probably still differences. But I ran through that a lot on a school laptop in high school. I'm not sure if I've beaten the genuine NES version before. I have it and have played it but by the time I owned it I had more interest in the current games so idk.