Hate to see this go unanswered. I'm no expert beyond a lecture course and an undergraduate seminar, but I’ll give my best.

The Byzantine system was definitively very complex. The state had an extensive aristocracy and bureaucracy which preserved a lot of practices and traditions from late antiquity and even earlier, along with newer Christian and Greek traditions and practices. There was also a significant amount of pomp, ceremony and tradition in all aspects of government. This kind of thing happens when a state is 1000 years old. However, their laws and practices, by the standards of today, were not especially complicated. In fact, it was also likely less complex than the systems of late Roman antiquity that came ahead of it; one of the major legacies of Byzantium was the collection and codification of Roman law in the Code of Justinian.

The origins of the negative connotations of the term Byzantine come from interactions with Western Europe during the medieval period, especially during the crusades. Simply put, many Western Europeans simply did not trust the Byzantines. Surrounded by hostile enemies for much of their history, the Byzantines were experts at utilizing diplomacy and often relied on the prestige, age, and complex ceremony of their empire to impress foreign diplomats. Also, the Byzantines were often quite willing to negotiate with and even side with Muslim forces where and when it served their interests. Western Europeans, used to a comparatively simplistic feudal system, simply did not understand all of this, because it was far outside their realm of experience. Also, their willingness to negotiate with “the infidel” left many Franks questioning which side the Greeks were on and whether they could be trusted. Generally, Greek Byzantines were stereotyped in the west as untrustworthy, effeminate and unwarlike. Of course, the Byzantines themselves tended to look down on the Franks, or Western Europeans, as uneducated barbarians (of course they literally were descended from the barbarians who had invaded and contributed to the downfall of the Western Roman Empire). This mistrust on both sides lead to several major incidents, the two most notable likely being the Schism of 1054 (about 40 years prior to the crusades and still at that time an ongoing and open issue), as well as the fourth crusade attack on Constantinople.

The term Byzantine as we know it to describe an overly complex and devious bureaucracy comes from around the 18th and 19th centuries. Many enlightenment and 19th century thinkers and historians were highly critical of Byzantium as a corruption of the once great Roman Empire, echoing the western medieval stereotypes of Byzantium in their criticisms.

For a TL;DR the modern connotation of Byzantine as being overly complex and devious is a result of western European stereotypes and misunderstandings in the middle ages and in the 1800’s, not of the Byzantine government actually being profoundly complex.

I’m sure there are some gross overgeneralizations here, but hopefully that helps some. My Master’s degree is in British Imperial history, so if a legit medievalist would care to weigh in here I’d love to hear more input.

Some relevant Wikis http://en.wikipedia.org/wiki/Byzantinism http://en.wikipedia.org/wiki/Byzantine_aristocracy_and_bureaucracy http://en.wikipedia.org/wiki/Corpus_Juris_Civilis http://en.wikipedia.org/wiki/East%E2%80%93West_Schism http://en.wikipedia.org/wiki/Fourth_Crusade

Edit: some grammer