UART Floating Voltage on Custom PCB?
It's pretty common to activate the internal pullup at least, and perhaps provide a stronger external one.  Floating inputs don't just cause false signals; an input near the logic level crossover voltage can cause a chip to consume excessive current, since both the upper and lower FET's can be partially turned on, causing a conductance path from the supply to ground.

For example, on an ATmega you can set the primary serial receive pin's internal pullup like this.

/* Idea copied from arduino bootloader - Enable internal pull-up 
resistor on pin D0 (RX), in order to supress line noise */
  DDRD &amp;= ~_BV(PIND0);
  PORTD |= _BV(PIND0);