Differences between Mario Bros for the NES and 25th Anniversary Super Mario Bros

The DS version's main feature is a few extra playable characters with special abilities. The Wikipedia article covers most of the functional differences.

However, I would like to bring attention to the main difference in my head: the DS controls are horrible. Since the DS doesn't have an analog stick, you are forced to use either the DPad or the stylus. Both controls are clunkier and more annoying than their 64 counterparts.

I loved the 64 version and got every star in it, and really wanted to play it again with new characters. Unfortunately, the DS controls made me unable to stand playing the DS version for more than a few levels in. It would be nice if they would rereleased the rerelease on the Wii instead so I have some chance of ever completing it. However, if you play it on a 3DS, you can use the circle pad in place of the DPad, which fixes all of those problems. On 3DS, the DS version controls just fine.

I have the problem myself and only have seen it in Skyward Sword, none of my other games show graphical issues. Some digging online shows it to be a hardware issue--your Wii's GPU is a bit fried. Not enough to ruin the graphics in other games, but since Zelda runs a more advanced graphical engine and pushes the Wii harder with depth of field effects it causes artifacts if you have a bad GPU. Nintendo can repair it, and that should solve the problem, but it may be a bit costly.

One thing to consider is the always-on nature of Wii's internet connectivity. Having the Wii on a constant 24 hours/7 days a week can bring it to a surprisingly hot temperature and probably wears out the hardware faster. Perhaps this touted feature was a bad idea, I can't help but wonder if doing this for 6 years caused my Wii's GPU problems.