Each step of serial correlation depends on another step. If the previous step includes a margin of error, that error grows with each subsequent step. This means as you work the formula, each answer can be further and further from the truth. The wide range for error makes it a difficult way to test the validity of the numbers or the accuracy of the formula.
Serial correlation only works in one direction. You can only utilize the factors when dealing with a 2D space. Time works very well as serial correlation because it only moves forward. For other items that can run vertical, serial correlation falls short. While you can still build a formula to test a theory, it is not entirely accurate due to the constraints you are putting on the data.
Serial correlation requires you know the true starting point of the data. Everything is dependent on what came before, so if you are missing the initial data point, your formula could be off base. Serial correlation works very well for data that begins at zero. Speed is something often tested with serial correlation. Numbers can come back lower, which is why economics can be built on the premise as the national debt is a serial correlation that just keeps getting worse, yet still only moves in one direction. If you are picking a problem up in the middle, you can decide on a starting point, but your formula might not be entirely accurate to encompass the whole problem.
The more variables you have in your formula the greater the opportunity for error. Because each number builds on the one before, you create an exponential growth in the error with each step and each variable. The variable differences create an even more problematic set of errors, as you must know the starting point for each variable to create an accurate formula.