This is not a historical question, but a basic few that pop into mind:

• Impracticality - Sometimes the branches can (or do) seize power anyways, by gaining support of the military and using it for themselves.

• Over-sized government - The government becomes large, too slow to act, and bureaucratic in going through its checks and balances on so many issues.

• Uncertain Checks - How many checks on each branch? Are there loopholes? They are possible, after all. Will there be an overseer for the overseers? How does that work?

There's plenty, but those are easiest to see in my eyes.