There have been some reports about problems, but the checkerboard while navigating a page can even be seen on the iPhone and other higher-end devices to a certain extent, if I am not mistaken. In addition to that, the ign.com front page seems to be more than 1 MB! Perhaps they should take this opportunity to optimize their code a bit? Browsing from mobile devices isn't actually going to become less common in the future.
The Hotmail problem is a complicated issue which also affects Opera on other platforms, and is at least partially caused by browser sniffing. If the DSi browser supports User JS, it might be possible to fix it that way. I don't know if Nintendo plans on updating the DSi browser itself in the future.
Gmail doesn't seem to be quite as huge as ign.com on first load, but there's a lot of advanced stuff going on, which could take its toll on the limited amount of memory available in the DSi. Let's see if it's possible to address this in some way.
In any case, considering the DSi's limited hardware, I think the browser looks quite promising. I haven't tried it myself, but I'm looking forward to giving it a try when it comes out here in Norway.
And I doubt that they would have been able to make any other browser run on the DSi hardware, so this says a lot about how versatile Opera is.