Points taken - I've updated the schematics and tested it, and the performance is much better.
The RC4580 opamp is more powerful than the other opamp but it also cannot drive 8 ohms headphones. What is the impedance of each ear of your headphones? Many headphones are 32 ohms and some are 600 ohms.
do I need a resistor at the output of the amp going to the headphones? I read that I might need one to prevent a short from frying the op amp when the headphone jack is inserted
The resistor reduces the power from a
power amplifier to headphones. Your RC4580
opamp does not have much power. A resistor is used in series with the output of an opamp that drives a capacitive load like a shielded cable (like the resistors to your line outputs) to keep it from oscillating.
If your output jack causes a short then use a better jack.
The RC4580 opamp does not have output current limiting so it will fry if its output load is too low (like 8 ohms) or shorted.
Also, I put in a 47nF (C6) cap in series with a 10Ω (R11) resistor at the output of the op amp going to the headphones because I saw it in an example circuit. Anyone know what the purpose of this is?
They are guaranteed to fry your RC4580
opamp, get rid of them.
They are used at the output of most
power amps to present a low impedance load at high frequencies when the impedance of a speaker is high due to inductance. Power amps oscillate without the resistor and capacitor. Opamps do not have enough output current to drive such a low resistance.
You have R2 feeding all the noise from the power supply directly to the mic input. R2 should have a 1k resistor in series and a 100uF capacitor to ground as a filter to it.
R7 does nothing and can be replaced with a piece of wire.