A long time ago, I read that the gravity force isn't the same if you are near the Andes Mountains or if you are at Paris. So today I asked to myself if when all continents were one, if the difference of gravity wasn't bigger. If there was no perceptible effect on the faune, on the rotation of the earth, and the tides. Maybe even on the motion of the moon.
You are quite correct that the position of the tectonic plates does affect Earth's gravity. The most accurate measurements of this were made by NASA's GRACE satellites. The results are generally shown as a geoid, that is a deformed globe showing where gravity is high and where it's low:
Note the scale is exaggerated to highlight the differences. The scale in the picture goes from -50 to 50 milligals, and 1 gal is about 0.1% of the average acceleration due to gravity so the maximum difference from the average is only 0.005%.
You ask about the effect on the Moon's orbit, and indeed this sort of effect is exactly how the maps shown above were obtained. The two GRACE satellites measure their relative position very accurately. When one of the satellites passes over a high gravity area (like the Andes) it speeds up slightly and the distance between it and the other satellite changes slightly. Measuring these changes allows the gravity to be measured.
So when a single supercontinent such as Pangaea existed it would have affected the motion of orbiting bodies. However the effects are very small, and at the distance of the Moon they would be immeasurably small.
You ask about the effect on Earth's rotation, and here I'm out of my comfort zone and have to resort to Googling like everybody else. Yes, there obviously would be a small effect on the rotation because the Earth would be asymmetric. However my guess is that the effect would be small. Remember we are talking about very small changes. Googling something like plate tectonics earth rotation will find you lots of articles on the subject.
It depends what accuracy you want to say things are equal. We often say $g=9.81 m/sec^2$ at the earth's surface and don't worry about it. Altitude and latitude affect this at the $0.3\%$ level. You can look at Wikipedia to start. Continental crust versus ocean crust is lower, but noticeable.
Isostasy is an important geophysical concept needed to understand the relationship of gravity, mass distribution, and first-order topography of the earth. The elevation of the ocean basins is lower than the continents because oceanic crust is thinner and more dense than continental crust. The gravity anomaly over a mountain range is less than you might expect if you do not consider that the crust adjusts in response to buoyancy forces and adjusts elevation by flow in the earth's asthenosphere.