The new handheld will support the DSi charger.
Nintendo has updated their Japanese Nintendo 3DS hardware page with more new details regarding their upcoming handheld. Andriasang.com has posted a translation of those details. Among them are the following:
The Nintendo 3DS will be compatible with the DSi and DSi LL charger. The DSi used a different charger than the DS Lite, which used a different charger from the original Nintendo DS.
Originally shown at E3 2010, Nintendo has confirmed the cartridge shape for the 3DS. The 3DS cartridges include an extra tab to prevent their insertion into DS systems. Below, you can see how the new cartridges will look in comparison to Nintendo DS cartridges.


Although it was already known that the 3DS would have increased graphical fidelity in comparison to the original family of DS systems, new screenshots released have given a metric for just how far the new system has come. Below are screenshots of Nintendogs from both the 3DS game, and the original DS game. While the top screen on the 3DS is 800x240 in resolution, half of the 800 pixels will be split for the left and right eyes, leading to a working resolution of 400x240.


Nintendo has confirmed that original DS games will not have any upgraded visuals when playing on the 3DS.
The Street Pass mode will support up to 12 games at any given time, without any of the games needing to be loaded for the feature to function. The transfers can be managed along with the parental controls. A game must have been booted at least once on the system for the Street Pass functionality to work.
Much like with the Wii, the Home menu can be accessed at almost any time (except when the system is using the wireless or camera features), which will pause the game.