multiple sumproduct criteria problem

What is the output you're getting ?

I think we would need to see a dummy sample to investigate.

Also, are you running XL2007 ? (as implied by your profile)

Rich, I think you mean:

=SUMPRODUCT((Incidents!$A$4:$A$500=$A$1)*(Incidents!$B$4:$B$500=B$2)*(Incidents!$C$4:$C$500>=$A3)*(Incidents!$C$4:$C$500<DATE(YEAR($A3),MONTH($A3)+1,1)))
EDIT: In attachment the above is incorrect as final test is <= and should be <

Note: in the above I've made the assertion that rather than typing "January" into A3 etc you've entered it as a date, ie 1/1/9 (format as "mmmm")

If using XL2007 you could use COUNTIFS which will be more efficient...(note also used EDATE which is auto available in 2007 but requires Analysis ToolPak activation in earlier versions)

=COUNTIFS(Incidents!$A$4:$A$500,$A$1,'Incidents'!$B$4:$B$500,B$2,Incidents!$C$4:$C$500,">="&$A3,Incidents!$C$4:$C$500,"<"&EDATE($A3,1))

Better yet of course would be to use a Pivot Table given this is what you're duplicating
Note: C56 on Incidents needed to be altered to become a date value - was/is text string

See attached wherein all 3 approaches are outlined... in order of preference in terms of Long Term efficiency & Flexibility:

1 - Pivot Table
2 - COUNTIFS (XL2007 Exclusive)
3 - SUMPRODUCT

The three you mention all occur in 2008... so the next question is are you looking to ignore by year - your initial formula did not imply as such..