While writing an answer about using multiple diodes connected to a single resistor, I stumbled upon a case about which I haven't read a lot: What happens when we set the resistor so that it sets the current to be within safe levels for a single diode and then connect several diodes in parallel to it?
The LEDs themselves should be safe from overload, becasue the current is limited. I expect that in the LED case, the distribution of current among them will not be equal since those with lower initial forward voltage will get more current and will be brighter. After a while the forward voltages will match and the current distribution will stay uneven.
Is there anything else that will happen? I've read the answers in this question and some of them mention oscillations, but don't elaborate on the topic.