Some interesting examples of incomplete thought here.

1) As regards rotation of the Earth and length of day:-

Sure, if we take the modern-day earth, note the tidal coupling to the Moon, back-integrate it to some starting condition, remove the Moon and forwards integrate, we get a faster spin.

HOWEVER - That initial fast spin was probably due in no small part to the off-centre impact which created the Moon in the first place. Without that particular impact, the Earth would have had much slower spin.

If you look at all the planets,, each one has anomalies in spin rate, or inclination of its axis, or eccentricity of its orbit that can be interpreted as remnants of an original chaotic assembly with late off-centre collisions.

2) Plate Tectonics:

At one time, I was working on the idea that plate tectonics became possible through the removal of thick primordial crust in that Moon-forming impact. Unfortunately, the idea doesn't work because although large amounts of crist and mantle material ARE ejected into orbit, 96% of it falls back to Earth again, restoring the status quo ante, at least in terms of bulk chemistry.

So my nice idea fails. :-(

Instead, you could call on that huge thermal event to kick-start intense convection in the Earth (as with the Lunar magma ocean), but that's just a timing thing. Even without the impact, the Earth would have assembled warm and quickly grown hot - after all, even the asteroids (much smaller than earth) show signs of differentiation including core segregation and in some cases basaltic volconism and aqueous fluids. And the Moon impact model requires the proto-moon (is it called Thea?) to have already differentiated its core, otherwise the whole scenario doesn't work.

3) "Sweeping-up asteroids" -

Well, the Moon has 1/81 the mass of the Earth (1/49 of it's volume) and 1/13.4 of its surface area. There is a mass-focussing effect (gravity) that lets bigger objects drag asteroids on near-miss trajectories into an actual collision, but even if we ignore this, the Moon is at best capable of intercepting 1/13.4 of the bodies that would otherwise hit the Earth.

So the basic argument is baloney.

You might argue that "because the Moon is spinning round and round the Earth it is better at intercepting near-miss trajectories", but this is a fallacious argument. For a start, that makes the Moon actually overwhelmingly likely to be in the WRONG place to intercept an Earth-aimed object. Also, it assumes that orbits are stable and permanent - the idea of clearing a sort of "tunnel" through a cloud of debris.

In fact, orbits are variable; and even for stable orbits, as we have seen with Skywatch studies and events such as 2004MN4, multiple possible intersections with an object exist with subtly different geometries each time - basically, it's random chance and bigger things get hit more often.

(We don't see surviving evidence for this because Earth has erased its primordial cratering record and even if it hadn't, all the terrestrial planets are saturated with impacts up to basin-forming scale, so they all look alike even if one had 2 or 10 times the impacts!)

4) It's all chance

Having shot the idea down in flames, let's ressurect it. With random events and evolution, a Moonless earth would be different. Not sure how. Assuredly "subtle" things like a completely different set of continents and history of plate tectonics. Maybe a slightly different radius, mass, gravity.

Also, a different history of impacts - No K/T dino-killer.

Come to that, no Dinos, per se. No mammals. No insects. Instead, a different random outcome of evolution's grand dice rolls. There might well be insect-like creatures, but they would be biologically different than the insects we know. (etc. for other life). Hell, even DNA could be different!

(Or if you're religious, simply think of it as a different God with a different set of designs)

Earth would be an alien planet if it had a different history, whether Moon-related or otherwise. Clearly the origin of the Moon is a major event in Solar-system evolution and has profoundly affected the earth.