The biggest issue (in the US national accounts, at least) is the fact that government production is recorded on a cost basis rather than a market value of output basis (due to the lack of market values for many government services).
From the NIPA Primer, pages 2-3:
GDP is composed of goods and services that are produced
for sale in the “market”—the generic term referring
to the forum for economic transactions—and of
nonmarket goods and services—those that are not sold in
the market, such as the defense services provided by the
federal government, the education services provided by
local governments, the emergency housing or health care
services provided by nonprofit institutions serving
households (such as the Red Cross), and the housing services
provided by and for persons who own and live in
their home (referred to as “owner-occupants”).
In cases where there are no similar market transactions
available to impute a value of the good or service being
produced, the output of these services is valued by estimating
the costs (such as employee compensation and
purchases of materials and supplies) of producing the
good or service.
As a result, any direct government production is recorded as though the workers add no value that they do not capture through their salaries. Given the technical difficulties (not to mention the political issues) that arise when one tries to come up with an alternative estimate of the value of government production, this is probably the most neutral approach, and the approach that is most accurate in differences, though it obviously gets the level wrong.