Given the size of the matrix - pre XL2007 you should really add a key to Errors sheet, eg:

Errors!L2:
="@"&A2&"@"&B2&"@"&I2&"@"
copied down for all rows
You can then use COUNTIF which is efficient whereas your alternatives are not.

Production!C6
=COUNTIF(Errors!$L:$L,"@"&$B6&"@"&LOOKUP(REPT("Z",255),$C$2:C$2)&"@"&C$3&"@")
applied to matrices
In XL2010 (as in XL2007) you could use COUNTIFS to negate need for Key

Without the key you are left with Arrays and/or SUMPRODUCT which are inefficient and should not be used in large quantity (as would be the case here) - assuming performance is of interest.