Our research lab has a benchmark spreadsheet (Excel) used to compare speed of
the computers we buy.  I can import this into OpenOffice just fine, but
OpenOffice Calc gives the wrong answers.

I believe that I know the correct answer, because I also have Mathematica to
compare with.

I have cut down the 256 column by 2500 row sheet to a 256 column 3 row sheet
which shows the problem.  (One could just copy the 3rd row all the way down to
recover my original benchmark).
 
A1=1.3
The first row iterates the formula Sqrt((cell to left)^2+1)
The first column iterates the formula Sqrt((cell above)^2+1)

The other cells have the formula of the form 
IV1==SQRT(IU1^2+1)  [ For the first row ]
IV2=Log10(ABS(BESSELJ(IV1;$A3)))+IU2
IV3=Log10(ABS(BESSELJ(IV2;$A3)))+IU3
In general:
cell=Log10(ABS(BESSELJ((cell above);(cell in same row, first column))))+(cell to
left)

OpenOffice eventually give error 502 in most cells.

The problem can still be seen with the simpler formula, which I am using for
this bug report.  Simply drop the call to Log10:
IV1=SQRT(IU1^2+1)  [ For the first row ]
IV2=ABS(BESSELJ(IV1;$A3))+IU2
IV3=ABS(BESSELJ(IV2;$A3))+IU3
In general
cell=ABS(BESSELJ((cell above);(cell in same row, first column)))+(cell to left)
Where the first row/column are still 1.3 or the sqrt iteration given above

Now the IV3 result (256th column, 3rd row) results are
Mathematica gives 30.0811386942866761144975205
Excel gives       30.08113874136690000000
OpenOffice gives 516.52017959013400000000

So you can see why I am distressed.  OpenOffice ends up wildly off,
while Excel is correct to 9 digits.

It would seem your BesselJ function is simply not getting enough digits
of accuracy compared with Excel.