I've seen it written that the run mechanic is sloppy, and requires you to hold the A button down.
While I agree that it is poorly implemented, you're not required to hold any button to run. If you just hold the directional pad down for a couple seconds you'll get up to running speed. It's crappy and not very Mario-like, but once you understand the mechanics of it the game is a bit more tolerable.
Just as a side note for those interested; this game has some strange TMSS/protection schemes going on that is making it very hard to dump. It's designed to skip the initial "produced by or under license" screen, and probably because of this the normal bootup routine isn't normal, so you can't use a SegaCD transfer cable (the game still boots even with the correct pin covered). It hides detection from normal copiers so they don't detect a cartridge inserted. The memory is made up of both chips and a globtops, so it's not a simple matter of desoldering and dumping a particular set of chips.