SNES:Vertical Line Fix
One problem that affects some SNES consoles is a vertical line constantly going down the center of the screen. The vertical line is most noticeable right when the console is powered on or in games with lots of dark scenes, such as Super Metroid. It’s believed the vertical bar is caused by the power drop during DRAM refresh; Essentially, an inefficient power filter.
Fix
Better Voltage Regulator
A fairly easy and efficient way to either remove or reduce the white line is by simply replacing the stock 7805 voltage regulator with one having a higher current rating, such as the ST L78S05CV-DG
Additional Improvement
Also, replacing the 1uF surface mount capacitor (C81) on the 78S05CV-DG's output circuit with a 22uF capacitor helps.
Alternative Fix #1
Instead of replacing the voltage regulator, you can try adding a capacitor to it. Add a 16v 470uF capacitor to the voltage regulator (which is attached to the heatsink), as shown below. Note the orientation of the cap and that the negative end (the side with the stripe) is connected to the center pin. If that doesn't work, you can try a 1000uF cap as well.
Alternative Fix #2
RGB Bypass mods can fix the white line on RGB out. If you have a 1CHIP (no RGB mod needed), or if you've already done the on-board RGB mod to a SNES Mini, then the above fix might be a better overall solution.
Alternative Fix #3
Use an SD2SNES. It seems the newer revisions of the SD2SNES ROM cart have an upgraded power filter, so the white line is _significantly_ reduced.