So I wanted to find out: what exactly is the bug in the program that causes this behavior and also, can it be fixed?

First I looked on the Internet to see if the answer has already been found. Some good starting information is located at http://www.jeffsromhack.com/products/donkeykong_tech.htm. There, Jeff Kulczycki breaks down the math of the kill screen, showing the formula that is used to compute the bonus for each level. The formula says the level times 10, plus 40, gives the number of hundreds in the bonus timer. If the result is too large it is forced back down. The key to this is that the level number is used in the calculation. On level 22 an overflow occurs, leaving the player with just 400 points on the timer because the multiplication and addition yields a number larger than 256.

» Don Hodges | donhodges.com