Problems:
Spain - The Umayyads (which is misspelled on the map) had been extinct since 1035. No reason to even have the name there at all. Islamic Spains was divided into at least several more petty kingdoms that I can think of right off the top of my head (including Valencia, Almeria, Ceuta and Denia). Mallorca wasn't independent, but part of Denia.
North Africa - the Almoravids had not yet conquered Fez by the end of 1066; it was an independent state until 1069. The areas ruled by the Zirids and Hammaids is vastly understated - they had indeed been driven virtually to the coast by Arab tribes launched from Egypt, but, although their situation was by no means rosy, it wasn't as bad as this map indicates.
Italy - Salerno is shown as far too large; the Norman holdings in Apulia and Calabria formed a continuous whole and weren't split by Salernian territory. Byzantine influence in the heel is a bit overstated; they had been down to Bari only as late as 1064, but had reconquered the ports of Brindisi and Taranto by the end of 1066, though the Normans for the most part ruled the hinterland, confining the Byzantines pretty much to those ports.
Balkans - Venice didn't own Split, the Byzantines did. Rashka was an independent state and should be shown separate, even though it was a Byzantine vassal
Russia - Novgorod, Chernigov, and Pereyaslavl were as separate from the central government in Kiev as Polotsk was. The Kievan realm no longer touched the Black Sea, being cut off from it by the Pechenegs and Cumans.
Middle East - The eastern Byzantine border is bizarre. It should be to the east of Edessa in the south; this city and all the land to its west that is shown as Seljuk were held by the Byzantines until after Manzikert in 1071. Byzantine rule is overstated in northern section of Armenia (The Kars/Erevan area); the west part of this sector should belong to Georgia, the east to local Muslim rulers. Seljuk influence is too far to the west; Aleppo and Diyarbakr had yet to submit to the Seljuks in 1066 and should thus be shown as independent. Interestingly the map shows Mazandaran as a Seljuk vassal, while not showing the realms of more important vassal states such as Mosul, Azerbaijan, Shirvan, and, most important of all, the Abbasid Caliphate. At least it separates Kerman from the main Seljuk state...
