I'm not referring to any physical aspects of a document such as age, type of paper, and the scientific methods used for authenticating those things. What I mean is the content itself.
In other words, if I were to write a first-hand account of the Battle of Fallujah in 2004, and 2000 years from now His Righteousness, Grand Emperor Zygbod IV's jet-pack-flying data-mining monkeys find it, how will they know whether or not I'm telling the truth?
Assuming their methods are the same as someone examining a supposed Roman legionary journal entry today....
Not to discourage anyone who wants to chime in, but there was an excellent discussion on using primary sources as a Monday Methods topic a while back. And here's the next in the series, about reading problematic primary sources.
Well, aside from those physical aspects you mentioned, which are part of the process, establishing the credibility of a source is really a matter of examining it alongside other primary documents. Is what your account says backed up by other accounts?
Now, firsthand recollections themselves are somewhat trickier than, say film from the battle, or a newspaper article from that day. Your memory of an event may differ slightly from somebody else's. So in your Fallujah example, it would be important to gather multiple such documents together in order to get a little bigger picture. Do all the accounts reference the same things? Do they reference things previously noted in secondary sources? Can you find some record that you, the author, were indeed a soldier who fought in Fallujah? As long as the "facts" all add up, you can work with that.
However, if you live on to become The Monkey Lord, Grand Emperor Zygbod I, you might be important enough to merit a biography, in which case your own account would be the one people were most interested in for writing that. Even if you made everything up, that would still tell historians something about you. What I'm saying is that what you're looking for in a source will vary some according to what it is you are trying to do.