flag missing categories within a group in an R dataframe

Question

I would like to flag itemid when the score variable is missing any score between 0 and max.score of that item. Here is an example dataset.

df <- data.frame(id = c(1,2,3, 1,2,3, 1,2,3, 1,2,3, 1,2,3),
                 itemid = c(11,11,11, 12,12,12, 13,13,13, 14,14,14, 15,15,15),
                 score = c(0,1,2, 1,2,2, 0,1,1, 2,0,0, 1,1,1),
                 max.points = c(2,2,2, 2,2,2, 1,1,1, 2,2,2, 1,1,1 ))

> df
   id itemid score max.points
1   1     11     0          2
2   2     11     1          2
3   3     11     2          2
4   1     12     1          2
5   2     12     2          2
6   3     12     2          2
7   1     13     0          1
8   2     13     1          1
9   3     13     1          1
10  1     14     2          2
11  2     14     0          2
12  3     14     0          2
13  1     15     1          1
14  2     15     1          1
15  3     15     1          1

In this case, itemid=12 is missing score of 0, itemid=14 is missing score of 1, and itemid=15 is missing score of 0 .

Any ideas on how to flag items 12,14 and 15?

Thanks!