Caps on MAX232 are not correct.
Should be 5 total - you only have 3.
MAX232 does not do USB to Serial - you need a part like FT232RL for that. See www.ftdichip.com
I would suggest a module like MIKROE483 from mouser.com $11
Also FTDI Basic or FTDI Breakout board
Or CP2102 module from e-bay, use the BATI kind that have DTR available at a breakout hole.
MAX232 will output +/-10V signals, and expects the same back. As drawn, T2out will blow up the Rx pin. And R2out will likely damage a PC if connectedl.
Put a diode across the reset resistor - anode to Reset, cathode to +5v.
What does cap C9 connect to when the jumper is closed?
C4 should be bigger, like 1 or 10uF.
C8 can be 1uF.
Add 0.1uF caps to the VCC, AVCC, AREF pins, as close to the pins as possible.
Can draw the VCC/AVCC parts next to C5.
JP5 - RTS should be DTR, I imagine you want it going to C9.
Check the order of the pins, make sure an FTDI Basic, or FTDI cable can plug straight on. I always double check against the ProMini schematic to be sure.