WiiConnect24 itself doesn't damage the GPU. It's the Standby mode, which you can turn off.

When you turn off your Wii, it goes into a Standby mode (red light). This is the default configuration when you first set up your internet connection. In Standby mode, your Wii stays online and can receive updates or download them overnight. Other people's Miis can also "mingle" on your system when you leave it on Standby. However, the flaw to this is that Standby mode uses a small amount of electricity, and has a chance of overheating the Wii, due to the fact that the fan is off. This is a minor problem, but sometimes it can overheat to the point where it damages the GPU.

This has happened to my system, but after I turned off Standby, it's been fine ever since.

@Cobretti
I am pretty sure there's green dots, cause I been seeing them a lot while playing Resident Evil 4, and after reading 200+ posts on it, I am almost certain that is GPU. I probably jumped a bit to conclusion on WiiConnect24 being on during standby as the cause, but it's the only one that make sense given the circumstance.

I recommend you try run a copy of Resident Evil 4, wait through intro movie till about the part where the policeman went down to pee till the car stops at the house and check if there's any green dots on there (or anything that shouldn't appear on the screen), if not, then you are fine.

@Kytiara
I am pretty sure I have the defect cause it's not just in intro movie I see that, but also in any dark environment, especially chapter 2 of RE4. I am not sure what artifact are possibly colored, mine is green. They are fairly small, I only notice it because my artifacts forms the outline of a rectangle (I originally thought it was the game), it might appear in my other games too, but they are quite bright colored, and no fog effect, so I can't notice anything. Resident Evil 4(Most Noticeable) and Legend of Zelda: Twilight Princess are apparently the only two games where this is noticeable in parts, and you need to look really close unless you get a big screen SDTV or a HDTV. I am not 100% sure at this point, this is simply my conjecture with my personal experience. I need to wait for some more information from Nintendo tech support before drawing final conclusion. I just thought it'd be better safe than sorry.

P.S. Resident Evil 4 mentioned here are Wii edition, not the GameCube edition (or so I've heard). I am not sure why, but someone suggested on another forum that is because the push on the hardware. (this is a guess, not a conclusion)

Edit: Yeah, what Cadence said. Although apparently GPU damage are permanent, and I am in the progress of checking this with big-N tech support. 

I guess I can see that. Unfortunately all electronic components, especially computer ones, are pretty sensitive to heat.

I'm wondering if the problem is an actual hardware defect or a design flaw though. I have my wii running in standby mode all the time and we've been getting 36-40 degree celcius heat lately (96-104 fahrenheit for you yanks) with no airconditioning at home =(. I've never noticed it getting that hot.

Anyway, sucks if this happens to you and I'll hope I don't see something similar =).

The problem is an overheating GPU. I had this happen on my Wii when I had one. It happened almost immediately after I purchased my PS3 and put it on the same shelf(the PS3 lets out a lot of hot air on teh top) so if you lay it on your side it will heat stuff up even if it is 2 feet or more away. the Wii got very very hot on the side facing the PS3. Than blotches on teh screen started to appear. It was what ever clor was on teh screen before the blotch appeared so if it happened on a black menu that blotch would stay black even if it si supposed to be wgite, red, green whatever. The more graphically intense the game the more it occured or if you play for a long time the problem got worse and worse until I called Nintendo and had it replaced immediately. the PS3 died 2 months later(but I suspect that was a firmware issue it crashed while installing the 1.6 firmware in mid march and never booted again.

takkxyz - thanks for that.

Cause I use toleave my wiiconnect24 on as well but turned it off a while ago cause the wii would get hot. Now its fine no head effecting the components.
WIll have to pick up resident evil 4 later.

Just got striekrs this week so yer have to wait till next pay.

The problem isn't so much that Wiiconnect24 generates a lot of heat so much as the fan is never active when the system is in sleep mode. The problem is, closed space + constant heat + little airflow. It doesn't much matter how little heat it generates it will keep building and heat is the natural enemy of any electronics.

My advice, if you're only gonna use your wii every few days, turn Wiiconnect24 off while in standby, it will help your wii survive longer. If you play actively like everyday, then chances are it won't really hurt you. Actually when I left wiiconnect on 24/7 it ran cooler when I played the wii then when it was in sleep mode which I thought was funny but it also caused me to just turn it off.

 That's what really irks me, I had a few day to busy to play the Wii, then this happens when I finally have some time... (Although I have little time again...)

I'm never fond of keeping appliances on stand by 24/7, not to imagine on an connect service like the WII. I always switch the entire console off when I go to bed or get out of the house. Even the WII can get pretty warm and when you switch it off, especially on 24/7 connect (yellow/orange) light, it continues to stay warm I've noticed.