Does the Earth revolve around itself with constant speed?

If the moon and sun are in different positions, it could change the speed, but the difference is very very small.

Plus there is a general slowing over time:

3. The Earth is slowing down

As a result of variation in gravitational forces due to the moon, the sun and other planets in the solar system, displacements of matter in different in different parts of the planets and other excitation mechanisms, the rotational speed of the Earth about it's axis varies in time. Recently, days have been getting shorter by hundredths of a second, which implies that the angular velocity of the Earth has been increasing. The factors causing this increasing in the Earth's rotational velocity have not been determined. The rotation data shows oscillations over several different timescales. The one with the largest variation is seasonal: Earth slows down in January and February. [1] [2] [3] "

http://fogonazos.blogspot.com/2007/06/ten-amazing-...

Rotational inertia. In recent history (the 20th century), humans have built a lot of dams and stored a lot of water at a higher elevation (farther from the center of the earth) than it would otherwise be. This is exactly like standng in the center of a spinning merry-go-round and moving toward the edge, the merry-go-round slows down. If you move back towards the center, it speeds up again. During ice ages, when a great deal of water was tied up in ice at the north and south poles (and ocean level was much lower than it is now) the earth turned more rapidly.