How much error in a transformation?

NADCON errors (NAD27) to (NAD 83) are in the range of 12-18cm http://www.ngs.noaa.gov/TOOLS/Nadcon/Nadcon.shtml. I think this answera a large part of your question. So yes multiple shifts can start to add up for high (very) quality survey data but it will take many NADCON shifts to start to meaningfully cause problems in most datasets.

The published accuracy of WGS 84 to NAD 83 for continental North America is 2 meters (http://support.esri.com/cn/knowledgebase/techarticles/detail/24159) with values lower than 2 in southern states and towards the top end in northern states. In Hawaii (4m) it increases as do other non-continental states. So yes multiple transformations can cause aggregated error.

The cross zones part of your question is fully answered at gis.stackexchange.com/questions/31701.

I think between these 3 sections your answer is complete.