I think you would have to redo most mapdesigns, because some compositions are set up for 4:3
you probably have to adjust the running speed, because traversing a screen might feel slower
more space on the screen means more to draw,w hich would require a more powerful machine / more RAM
on a bigger screen possible you need to display more sprites, which also might have a ginificant impact
same goes for parallax layers.
for topdown games the n/s direction might be much smaller than the w/e directions than in 4:3 which either has to be accounted by gaedesign, leveldesign, or the overall game formula.
A characte rmight feel a lot smaller on a 16:9 screen than on a 4:3 screen
maybe you would need even differently drawn characters.
Mos tlikely there are a ton more challenges, you would come across once you really try it.