50 Amp tankless water heater and 30 amp double pole switch
I am going to try to brake down your question.


  I have a 60 amp max tankless water heater.


Now just off of what you said the 2014 NEC Table 310.15(B)(16) shows that a #6 or #4 wire is needed for 60 amps, depending on which wire you use. 


  The circuit breaker is 60 amps.


You are right in line with the amps of the water-heater.


  The water heater is connected to a NEMA 10-50 power receptacle


That receptacle is only rated up to 50amp but try to find a 60amp 3wire receptacle.


  There a switch to turn on and off the water heater from inside the house. I am going to replace the switch. I noticed that it is a double pole 30 amp switch.


BIG problem, the switch is way under sized, but from your picture it doesn't look like the correct size wire ether. 

I would look at the wiring that is going to the breaker and see if it is correct. You may have to start over again.