As metioned earlier by kchriste don't forget the 100nf capacitor across the pic power pins 19 / 20 - should be fitted as close to the pics pins as practicable - would be good to fit one across pins 9 /10 of the 2803.
Apart from good design pactice to fit one to each ic used, they will help with the poor usb power rails.
hi,
As you have only 4 relays to drive, a transistor drive/relay would be a better option than a ULN, because of the tight voltage margin.
A 2N2222 transistor will give a Vce of about 0.2V and without the series +5V diode, it would give approx 4.8V across the the 5V relay coils.