The book begins by outlining what the Three Mistakes are.
Chapter One begins:
To be able to fully comprehend the changes that will be proposed, one must first be able to understand the current working method of official handicapping. Be it traditional weight handicapping or modern speed handicapping, the official Beaten Lengths Adjustment Chart applies to all. 

This Chart gives the handicapper a guide to the number of pounds to deduct from the winner’s rating according to the aggregate distance said horse finished behind the winner. The Chart caters for all distances, from a five furlongs dash to a twenty-furlong slog. To know how this Chart is compiled we must know how to calculate the pound value of one length. 

The modern Thoroughbred horse is said to weigh 1,100 pounds. Five furlongs is equivalent to 3,300 feet. Therefore it was declared that three feet corresponded to one pound. The Thoroughbred was stated to be nine feet long when in full stride. Hence, one length (nine feet) was acknowledged to be the same as one pound. Here are the calculations:

1 furlong = 660 feet and 5 furlongs = 3,300 feet
Weight of a Thoroughbred = 1,100 lbs.
Length of a Thoroughbred in stride = 9 feet
3300 feet divided by 1100 lbs. = 3 feet per lb. 
9 feet divided by 3 feet per lb. = 3 lbs. per length
This is quite elementary so far. Now, the pound value of a length needed to be calculated for each distance. From the above workings it was seen that:
No. of furlongs x Pound value of one length = 15
So, using simple calculations, the following table can be deduced for the pound value of one length at stated distances:
 
Distance (furlongs) Pound value of 1 length
5 3.00
6 2.50
7
2.14
8
1.88
9
1.67
10
1.50
11
1.36
12
1.25
This was how to calculate the number of pounds to deduct from the winner if a horse finished one length behind. A chart was then needed for each distance to illustrate how many pounds needed to be deducted for each beaten distance.

Later in Chapter One we come up against a problem; a former jockey, now a steward, came up with the following calculation; 1 second = five lengths. The reasoning behind this formula is strange:

The most common standard time for five furlongs is one minute. So:
5 furlongs = 3300 feet, and 1 furlong = 660 feet
1 minute = 60 seconds and 60 seconds divided by 5 = 12 seconds per furlong
660 divided by 12 = 55 feet per second
Because 1 second equals 5 lengths:
Then it must follow that:
5 times the length of a Thoroughbred in feet = 55 feet
Here the stewards must have come up with the ‘new’ value for the length of a galloping horse. 
The length of a Thoroughbred in stride is now 11 feet.
Three Mistakes then goes on to tell you how to put these errors right, and how to calculate a ratings formula based on pure science that is different to any other method.