Replaced my dome light with an LED. No issues so far, and it dims properly, but depending on how it dims (pulse-width modulation or voltage) it might dim erratically. Some system might fuss about burnt out bulbs, but I doubt in the interior such a system exists on any car (if you can't figure out a bulb is burned out when your car is dark inside, a warning light won't help you).
Turn signals on LED's need mods to the flasher unit usually, since most have a doubler so you get that "fast flash burnout" mode.
Biggest issues?
Mounting new lights (mine replaced a festoon bulb with a small 48 LED wafer. I needed to build a little mount for it out of balsa wood to fit it inside the dome cover. The stock setup was just a peice of two sided foam which immediately fell apart from the heat from the bulb. Its not "hot" but hot enough to).
Also the LED I bought was insanely bright (by insane I mean, I can light up a ditch outside the [censored] car with my dome light) and people always telling me how insanely bright it is, but its better then staring at the floor in a pale light fighting to see something. I can pretty much disassemble a Swiss watch in my car with ease, its great.
Only other issue is the LED gives off ultraviolet light I think, or maybe just because of the brightness, but insects love the thing. I have left it on all night long by accident and it didn't kill the battery, so that was also a bonus.