With native control on, Nintendon't on the Wii (not Wii U, I have yet to test this on the Wii U) has no (known) issues for Melee that are game changing. Nintendon't has no input lag from my tests, so if you're getting some it's probably display lag from your TV or monitor (or controllers if they are Bluetooth, which would be around 6 frames of lag).
Nintendon't has far less problems than DIOS-MIOS, and unlike the latter mentioned, is still being improved. In response to the post above that mentions of 20XX crashing, that's probably the ISO's problem. You may have built it incorrectly, or added extraneous things (ex: custom music) to it. 20XX is prone to crashes and is relatively unstable with any booting method.
The only problem Nintendon't has with Melee is loading HPS files at times, which is the file type Melee uses for it's music. Sometimes there is minor beeps, but that's literally it. Some hardware like the Gameboy Player/GBA-Link Cable/Modem support is not supported by Nintendon't as well, but this is due to the Wii/Wii U's hardware limitations. The hardware may be emulated in the future.