Issues with a timing circuit using a comparator and RC
The output is a transistor (NPN) to ground i.e. open collector so if you calculate 270 ohms for the LED, connect the LED directly to the output of the comparator and use a 270 ohm pull up. Having the 470 ohm in series with the 270 ohm will make the LED much dimmer.

If you want to be more economical with power, wire the LED in series with the 270 ohm from output to power rail then, when the comparator output is "open-circuit", there will be no current taken by the output stage. You might have to swap inputs around to give you the correct functionality now.

I'd use a non-polarized capacitor such as ceramic but a tant would be fine. 

For more accurate and repeatable timings the 6.2 Mohm discharge resistor is possibly a little too large given that the input bias current could be as high as 0.5 uA (over temperature). I tend not to use resistors greater than 1 Mohm if I can so maybe next time consider a better comparator.