Almost - don't connect Aref to +5, just a cap to Gnd. It has internal connection to +5, or +3.3, under software control.
Connect pin 7 to 20.
This where a view of the schematic comes in handy.
If you can do a ground pour, or ground fill, or whatever the program you are using calls it, then you can delete the all over the place ground traces and just connect those pins to the ground plane instead. That will make for quieter signals too.
You have room on the board - I would add a diode in parallel with the reset resistor - anode to the reset pin, cathode to +5. This will keep any spikes that occur from making the chip think its going into High Voltage programming mode (and look liket its just hung up to you). 1N4158 type of diode is sufficient.
Looks like you have 2 regulators? Would recommend caps on the 2nd regulator also. 1uF on input, 0.1uF on the output.
Do you have any plans to add pin names (D0, D1, etc) or part names (C1, C2, etc)? That really helps to make the boards look sharp.