I gave 1.5.1 a full playthrough.
The only issue I found is in the File Select Screen.
If you go from Mario -> Luigi and then try to go back to Mario, the game kicks you out to the Title Screen.
One other thing (though I'm not sure if it's emulator specific or RetroArch's fault) is that whenever I tried to savestate and load, the game would load whatever state Mario/Luigi were last in before loading the state. Like if Mario has been killed, the state would load Mario being killed, even if there are no enemes around.
Same for when you have powerups, if you had a Fire Flower on the savestate and you try to load the state with Mario being small, when the state loads, Mario will be tiny.
All tests were done on mGBA 0.6.3 core through RetroArch.