I cut my gaming teeth on the N64 and PS1, so I haven't played this game all that much. In fact, the first time I ever actually owned it was on 3DS through the Ambassador program. I haven't beaten it, but I also haven't really put in the effort. I think the save-state I have used no warp zones, but it did use the continue code. Mostly because I play that game in particular very carelessly, constantly moving forward and with the B button practically glued down, even if I don't know the level. The last stage I remember making it to was a castle that I got stuck on because I didn't know the path sequence and got it wrong too many times and ran out of time. I didn't feel like doing any more trial and error, so I put it down for a bit.
It's relatively easy for an NES game, but it's still harder in some ways than many popular modern games. Part of me thinks that there were more hard games back then that were popular because they were still simple to figure out the basics. Like, sure we can call a modern FPS campaign on normal difficulty "easy", but just the act of moving, viewing, and interacting with the world is much more complex with the dual analog, aiming, shooting, reloading, and all the rest. SMB's basic actions are: walk, run, jump, chuck fireball. Literally every possible interaction between Mario and everything else in the game can be described by one of those (and collision in general).
EDIT: PK Gaming, there are literally infinite continues. Just hold A and press Start after a game over, and you'll start back on the first level of the world. (i.e. start at 4-1 if you died on 4-4)