Earth and moon have different mantle compositions. Is this a fatal flaw in the 'Giant Impact hypothesis'?
I highly recommend this blog article from the Planetary Society. It is from 2012 but I believe the science is still sound. The author herself, has received recognition for her contribution to communicating space science to the public (She has an asteroid named after her!!)

It doesn't address your question about if there is a flaw in the giant impact hypothesis through an isotopic analysis, but rather through a gravity anomaly analysis from the GRAIL Mission.


Isostasy, gravity, and the Moon: an explainer of the first results of the GRAIL mission. Written by Emily Lakdawalla, 11 December 2012


The article starts off by giving some information on how gravity anomalies are formed and measured, before delving into the main arguments.

In Summary (all mistakes are mine), using various analysis's of the gravity anomalies, resulting in 3 further scientific papers linked in the article, the GRAIL mission has determined that the Moon has a highly fractured and highly mixed crust. The crust is alot thinner than previously thought and in some places the crust is nearly or even 0 km deep, allowing mantle minerals to be exposed on the surface. The unexpected porous nature of the crust supports the Earth/Moon common origin, whereas before there was a mismatch in the assumed numbers giving some doubt to the giant impact hypothesis. 

The article then finishes off by mentioning an existing theory on how the moon could have formed while still creating the observed features we can see today.



About halfway through the article, after discussing Airy and Pratt Isostasy, the article starts to mention the observed results. When looking at the Bouguer gravity of the Moon,


  Now, the Moon should have local, small-scale variations in crustal density due to local geology; the fact that the variations are small and smooth means (Zuber argued while presenting these results) that impact cratering has completely battered, bashed, fragmented, mixed, and remixed the upper couple of kilometers of the crust, totally homogenizing it. Previous maps of lunar gravity have not had high enough detail to see this beautiful match between topography and gravity; so this is a new GRAIL result.


a little further on discussing some more results about the density of the moon surface,


  There is one big very surprising thing about this map. The average density is 2550 kilograms per cubic meter. This is much, much lower than what has been assumed for lunar crust; in fact, it's lower than the density of granite. We know what the highlands crust is made of, we have samples of it: the density of the minerals that makes up the crust is around 2800-2900 kilograms per cubic meter. For the Moon's density to be so low, Wieczorek says, it must be very porous, fractured and busted up to give it about 12% void space, to a depth of several kilometers below the surface. This is an important GRAIL result. The mission has given us X-ray vision to see that the Moon's crust is absolutely shattered from the surface for thousands of meters down. In places where the crust is very thin, even the uppermost mantle may be fractured and porous.


Here is where the article starts discussing the mantle minerals, especially Olivine which you mentioned. (emphasis is mine)


  This map shows crustal thickness is near zero under a few of the impact basins (particularly Crisium and Moscoviense) and some of the deepest craters inside the south pole-Aitken basin (Humboldtianum, Apollo, and Poincaré). And the crust reaches a high of 60 kilometers on the farside. Kaguya compositional data support the GRAIL conclusions. There's evidence for the mantle mineral olivine being exposed in precisely those places where GRAIL sees the thinnest crust: Crisium, Moscoviense, and Humboldtianum.
  
  The average crustal thickness that Wieczorek and coworkers calculated, 34-43 kilometers, is much lower than has previously been assumed. Why is that important? Because when you work out the math to figure out what the bulk composition of the Moon is, given this thinner crust, you wind up with numbers for the abundance of aluminum that are a much better match to Earth's aluminum abundance than they were before. Previously, an apparent compositional mismatch had been a problem dogging the giant impact hypothesis for the Moon's formation. The GRAIL result makes for a compositional match.


Near the end of the article, The article mentions Sean Solomon's idea on how the moon could have formed.


  Andrews-Hanna pointed out that some theorists have predicted exactly this situation. The paper he cites was by Sean Solomon, principal investigator on the MESSENGER Mercury mission, who was trying to explain how Mercury could have wrinkle ridges caused by global contraction if the Moon does not.
  
  If you condense the Moon from a ring of debris orbiting Earth following a collision, the first nucleus of the Moon will actually be quite cold. As it grows, the increasing energy of the impacts of stuff onto the proto-Moon would make the Moon's mantle hotter than its deep interior; you could wind up with a cool, solid center surrounded by a hot, liquid mantle. The heat from the mantle would take time to propagate into the interior; as it did, the warming center of the Moon would expand, producing exactly the kind of global extensional stresses that could make this set of dikes. The model has this expansion happening at the correct time, too: before the Moon was 500 million years old, which would be before the end of the basin-forming impacts.




I hope I actually understood the article correctly and that it helped answer your question. Albeit through a different route.