The DoD has a general policy that government owned computers should not be used for personal (i.e. nongovernmental) reasons. However, that policy also allows for appropriate authorities to permit limited personal use on a "not to interfere" basis - as long as it doesn't use too many resources (bandwidth, cpu time, etc.) or cost too much money or waste 'working' time. Most military polices on computer usage will have this boilerplate exemption, which is similar to "incidental loss" policies that keep people from being prosecuted for taking home a "property US Government" pen. Thus, it is usually (though not always) permitted to check personal e-mail, web surf, etc. during "break time" or off duty. These activities are further limited by policies against things like pornography and other materials/acts deemed contrary to "moral and good order'.
As to the base name being included on documents it depends. Was there an intentional attempt to mislead people about these being "official" government documents? Or was the name simply included on a print-out as an oversight or even part of a simple factual statemement? (i.e. "This e-mail viewed an printed out at location XXX on date YYY").
Perhaps more directly, if someone who is suing you uses the government computer/printer for relatively minor documentary purposes, it is highly unlikely that you can get them into legal trouble.
