For most players a bad session is
1. when you lose money
For good players a bad session is
2. When you make mistakes
it is that simple
Yep, the above is true. I look at my bad sessions and nearly always find mistakes (and tag them as so). I tag bad beats and unfortunate hands also. In most of these sessions, I find if I had not made mistakes, I would have made money, or broke even.
Your question, how do you know you are having a bad session? A bad session for me is a combination of two of the following:
1. Long periods (1000 hands or more) of poor starting hole cards. This is when it is very noticeable that you have not been getting many premiums, or playable hands. Usually you are folding pretty much constantly.
2. Unusual amount of missed flops. These are card dead periods lasting a few hours. I measure these using hit flop ratio statistic. Usually for unpaired hole cards this is ~32%. Last night for example I played 1500 hands in cash games and I hit the flop 16% over the whole session.
3. Greater than 5 large pots lost per 2 hours due to bad beats, unavoidable coolers and suckouts. Many times I have been playing to make back money lost early in a session. Other times I am finishing with 5BI instead of 10BI due to bad beats/crap luck toward the end of my session.
That's for me anyway, but the quantity you play will have an effect also.