Q:

Are there cases or arguments where the Truth Table is not reliable?

Below is a basic Truth Table where p can represent the first argument and q for the second argument.
+-----+-----+-------+-------+
|  p  |  q  | p ∧ q | p ∨ q |
+-----+-----+-------+-------+
|  T  |  T  |   T   |   T   |
|  T  |  F  |   F   |   T   |
|  F  |  T  |   F   |   T   |
|  F  |  F  |   F   |   F   |
+-----+-----+-------+-------+

Suppose that we use the operators AND ∧ and OR ∨ to verify arguments like so:
p - Samson is longhaired
q - Petrucci is longhaired
p∧q - Samson and Petrucci are longhaired
This works well for the above example.
However, are there cases where the truth table is not reliable as a basis for proving the validity of arguments?

A:

Truth tables are used to define what validity is. For that reason, they cannot fail to be reliable indicators of validity.
There may be cases in which what seems intuitively invalid comes out as valid according to the truth table. In these cases, you will likely want to examine your intuitions or make some clarifications as to your language.
For example, this might happen if you treat a counterfactual conditional in the same way as a normal conditional. In this case, people considered the matter and decided that the intuitive problem was due to the counterfactual nature of the conditional, not to a problem with the truth table. 
Philosophers are very reluctant to conclude that truth tables are not guides to validity because they are definitional of what validity is, so challenging them would require a wholly new conception of validity (not that there aren't such conceptions around, but I assume that's outside the scope of this question).

