Why is 3333360 the maximum score in Pac-Man?

The score is limited because a glitch occurs on level 256 which overwrites half the screen with garbage. The game won't let a player advance from one board to the next without eating 244 dots and energizers, but the glitch overwrites many of the dots; this will leave the player unable to eat 244 dots and energizers, and thus unable to leave the level. In case you're wondering about why the glitch occurs, the machine code in Pac-Man to draw the fruits is similar to the C code:

unsigned char temp1, temp2;
unsigned char *ptr;

temp1 = level;
if (temp1 > 15) temp1 = 15;
temp2 = temp1;
if (temp2 > 7) temp2 = 7;
ptr = LOWER_RIGHT_ADDRESS;
do
{
  *ptr++ = shapes[temp1--];
} while(--temp);

Note that unlike many machines, Pac Man uses a rather curious screen memory layout which places consecutive bytes horizontally on the top and bottom of the screen, and vertically in the middle. This was most likely done to make it so that when drawing the main portion of the screen, memory addresses would be incremented by a power of two every eight scan lines (note that the "top" of the monitor is at the right side of the picture). Essentially, circuitry converted row/column indices to memory addresses with a mapping similar to:

//Using column values in the range 30 to 1, wrapping after 63...
address = (column & 32) ? 
          (row << 5) | (column & 31) :
          ((28 | (column & 3)) << 5)  | row);

but implemented in circuitry rather than code. This allowed screen addresses to be computed by using a pair of counters and a circuitry to select one of two permutations of those counters' bits. The hardware required to have memory address increase by 36 for each row rather than 32 would have been more complicated by comparison.