For some reason, this happens to me both when choosing ottoman, and when meeting him in game. It seems to be some sort of bug with the leaderhead.
You can "fix" it by substituting another leaderhead for mehmed in the Assets\XML\ART\CIV4ArtDefines_Leaderhead.xml file.
I used the leaderhead for stalin, so you can substitute this code for mehmed's code:
<LeaderheadArtInfo>
<Type>ART_DEF_LEADER_MEHMED</Type>
<Button>,Art/interface/LeaderHeads/Btn_LH_America_Washington.dds,Art/Interface/Buttons/Warlords_Atlas_2.dds,2,8</Button>
<NIF>art/LeaderHeads/Stalin/josef_stalin.nif</NIF>
<KFM>art/LeaderHeads/Stalin/josef_stalin.kfm</KFM>
<NoShaderNIF>art/LeaderHeads/Stalin/josef_stalin_noshader.nif</NoShaderNIF>
<BackgroundKFM>art/LeaderHeads/Stalin/josef_stalin_BG.kfm</BackgroundKFM>
</LeaderheadArtInfo>
This is on line 297 in my file. Hope this helps!