Relay switching problem with ATmega328P + 10 relays
I can see lot of problems.


No decoupling capacitors on ATMega.
Capacitors on both sides voltage regulators are usualy essential for regulator stability. 
Big voltage drop on regulator - if it's overheating, thermal shutdown might happen. For example 7V drop @ 350mA (about four relays) results into 2.45 Watts turned into heat.
Bare HC06 doesn't like 5 Volts on its 3.3V logic level input
Xtal oscilator usualy requies two capacitors (22pF) for better stability.