WRONG
We would appreciate if you corrected the entry in the register as soon as possible.

RIGHT
We would appreciate it if you corrected the entry in the register as soon as possible.

This is a very common mistake, and I think I have seen such sentences written incorrectly more times than I’ve seen them written correctly.

Remember that when you use the phrase “I would appreciate…” you MUST include the word “it” before “if”:

I would appreciate it if…

More examples:

WRONG
As you will be contacting the company yourself, we would much appreciate if you could inform us of the result of your enquiries.

RIGHT
As you will be contacting the company yourself, we would much appreciate it if you could inform us of the result of your enquiries.

WRONG
I am sure the supervisory authority would not appreciate if you took that course of action.

RIGHT
I am sure the supervisory authority would not appreciate it if you took that course of action.

WRONG
We would appreciate if you would arrange for immediate payment.

RIGHT
We would appreciate it if you would arrange for immediate payment.

There is no need to add “it” if you do not include “if”. E.g.:
We would much appreciate a letter informing us of the result of your enquiries.

I am sure the supervisory authority would not appreciate that course of action.

We would appreciate immediate payment.

An alternative phrase to “I would appreciate it if…” is, of course, “I would be grateful if…” This is the more formal phrase of the two and does not require that troublesome “it”!