[EvaH (OP)]

Colin wants to know:

The moon is moving away from the earth as it gains angular momentum from the Earth. Does this mean the Earth is slowing down? If so what are the consequences?

What do you think?

[Halc]

The moon is moving away from the earth as it gains angular momentum from the Earth.

Correct, and this seems to answer the question in the title.

Does this mean the Earth is slowing down? If so what are the consequences?

The spin of Earth is slowing down, since that is from where said angular momentum is being taken. The consequences are longer days over time.  The Earth used to take ~10 hours to make one rotation.  It is now nearly 24 hours, and given enough time and lack of interference, will eventually lengthen to about 1500 hours, at which point Earth will have no more angular momentum to give the moon.

[Janus]

Colin wants to know:

 Does this mean the Earth is slowing down? If so what are the consequences?

The is increasing its period of rotation at a rate of 1.7 milliseconds per century ( every century it takes an additional 1.7 milliseconds to make one full rotation.)
One consequence of this is that we have to adjust our clocks every once in while in order to keep them in step with the Earth.
While the length of the second was once based on a certain fraction of the how long it took the Earth to rotate, once we learned that this rotation was not constant, rather than constantly changing the length of the second, they changed to a standard that doesn't change over time.( for one thing, many physical constants are based on the sec. Constantly changing the second would mean having to constantly change the value of the constants)  This switch was made ~60 years ago.  During which time, the length of the Earth's rotational period has lengthened by a bit over 1 millisecond.  Now, while this might not seem like enough to worry about, remember, this is per day, and this difference accumulates.  Every day, our clocks and the Earth's rotation would drift 1 millisecond further out of sync.  After 1 yr,  they would be over a 1/3 of  second out of sync, and in less than 3 yrs, they would be 1 sec out of sync.  In order to keep this from getting out of hand,  every so often we adjust the official time by adding a "leap second", which re-synchronizes out clocks to the Earth.*

*These are just illustratitive numbers, as the chosen length for the sec was not based on the rotation period of the Earth at the the time they set the standard.  Also, other factors can effect the Earth's rotation. For example, the 2004 earthquake that caused the Indian ocean tsunami, shifted the Earth's mass enough to have a effect on its rotation.   All this has to be taken into account when deciding if and when to add a leap second.

[evan_au]

There is a nice graph and table of all the official leap seconds here:
 https://en.wikipedia.org/wiki/Leap_second#Slowing_rotation_of_the_Earth

[hamdani yusuf]

The Earth used to take ~10 hours to make one revolution.

I believe you meant rotation.