I think there are still a few games that still aren't properly compatible, and DSi Enhanced games don't work in DSi mode yet. Real carts can do both, obviously, and most flash carts don't have compatibility issues at this point.
However, at this point, running from SD is pretty viable. I've tried many games without issue, with the most I've had to do being to keep my settings a certain way as a base (don't even need any special per game settings for anything I've tried yet).
This is my settings layout if you're curious, as it seems to be the most compatible set up for me:
Run in: DS mode
ARM9 CPU Speed: 133 MHz (TWL)
VRAM boost: On
Force sleep mode patch: Off
Slot-1 launch method: Direct
Sound/Mic frequency: 32.73 KHz
From what I can tell, if a game seems to be fully working, it very well may be. Compatibility is pretty high at this point. Some people still seem to encounter freezes or long load times in-game, but I've tested some of the same games without issue, so it may be misconfiguration, a bad dump, or something like that.