[java] Rock, Paper, Scissors Game Java

Before we try to solve the invalid character problem, the lack of curly braces around the if and else if statements is wreaking havoc on your program's logic. Change it to this:

if (personPlay.equals(computerPlay)) {
   System.out.println("It's a tie!");
}
else if (personPlay.equals("R")) {
   if (computerPlay.equals("S")) 
      System.out.println("Rock crushes scissors. You win!!");
   else if (computerPlay.equals("P")) 
        System.out.println("Paper eats rock. You lose!!");
}
else if (personPlay.equals("P")) {
   if (computerPlay.equals("S")) 
       System.out.println("Scissor cuts paper. You lose!!"); 
   else if (computerPlay.equals("R")) 
        System.out.println("Paper eats rock. You win!!");
} 
else if (personPlay.equals("S")) {
     if (computerPlay.equals("P")) 
         System.out.println("Scissor cuts paper. You win!!"); 
     else if (computerPlay.equals("R")) 
        System.out.println("Rock breaks scissors. You lose!!");
}
else 
     System.out.println("Invalid user input.");

Much clearer! It's now actually a piece of cake to catch the bad characters. You need to move the else statement to somewhere that will catch the errors before you attempt to process anything else. So change everything to:

if( /* insert your check for bad characters here */ ) { 
     System.out.println("Invalid user input.");
}
else if (personPlay.equals(computerPlay)) {
   System.out.println("It's a tie!");
}
else if (personPlay.equals("R")) {
   if (computerPlay.equals("S")) 
      System.out.println("Rock crushes scissors. You win!!");
   else if (computerPlay.equals("P")) 
        System.out.println("Paper eats rock. You lose!!");
}
else if (personPlay.equals("P")) {
   if (computerPlay.equals("S")) 
       System.out.println("Scissor cuts paper. You lose!!"); 
   else if (computerPlay.equals("R")) 
        System.out.println("Paper eats rock. You win!!");
} 
else if (personPlay.equals("S")) {
     if (computerPlay.equals("P")) 
         System.out.println("Scissor cuts paper. You win!!"); 
     else if (computerPlay.equals("R")) 
        System.out.println("Rock breaks scissors. You lose!!");
}