I've now received the 1st 100% correct solution to the lsd radix sort!!!
To encourage you all to go ahead with the msd version too I'll give you
an extra 25% bonus for getting them both.  That is, the max score will
be 125 rather than 100.  You can send them one at a time or both together
as you please.  In order to catch some of the errors which manage to
end up with the same values spread over the entire array it is helpful
to change your main() and check_order() functions as follows

...
main(int argc, char *argv[]) {
        int i, nvals = 10000;
        unsigned int *array;
        if(argc > 1)
                nvals = atoi(argv[1]);
        array = malloc(nvals * sizeof(unsigned int));
        for(i = 0; i < nvals; i++)
                array[i] = rand();
        check_order(array, nvals);
        lsd_radix_sort(array, nvals);
        check_order(array, nvals);
}

int check_order(unsigned int *ip, int n) {
        int i, sum = 0, nrev = 0;
        sum = ip[0];
        for(i = 1; i < n; i++) {
                if(ip[i-1] > ip[i])
                        nrev++;
                sum += ip[i];
        }
        printf("checksum %d\n", sum);
        if(nrev)
                printf("%d misorderings\n", nrev);
        else
                printf("array is in order\n");
        return(nrev);
}
...

This will run the check_order() both before and after you have done the
sorting procedure.  Before sorting the array should be about 50% out of
order and of course completely in order afterwards.  Also, no matter
what the order is, you should get the same checksum before and after
as long as you have not duplicated any numbers etc.  Therefore, this
is a more robust error check.  Your result should be similar to this...

[awetzel@europa /tmp]$ time a.out 100000000
checksum 563608529
50000280 misorderings
checksum 563608529
array is in order

real    0m40.853s
user    0m35.110s
sys     0m5.740s