if I let's say take 64bits and simply shift them back and forth for let's say 5 billion cycles, can I be sure that non of the bits was shifted incorrectly?
Extremely low. The microcontrollers generally work in 8 bit chunks since they're 8 bit CPUs. Lets say for simplicity that that 64 bit operation is actually 8, 8 bit shifts. Each shift is one CPU instruction. Lets say 2 more instructions to accomplish the loop. So 10 instructions.
5000000000 * 10 = 50000000000 instructions executed. AVRs execute 1 instruction per clock cycle so that is 50000000000 clock cycles. 50000000000 cycles / 16000000 (16MHz) = 3125 seconds or 52 minutes.
It would only take 52 minutes for an AVR to perform 5 billion shifts of 64 bits of data. The chance of error in 52 minutes of operation is extremely tiny unless the power supply is poor or the clock is glitchy.